To get natural looking modeling on a face its necessary to get the lights above the head, because that is where most natural and indoor lighting comes from. Next let one more dominant "key" light source define the 3D shape of the face with a pattern of highlight and shadows.
The role of fill is to lift the shadows of the key light up to where the camera can record detail in them. While it might seem logically to just put a light on opposite side for fill that turns out not to be very flattering light for portraits because one light cancels the other and both create opposing shadows. Note the weird nose shadow in the first shot? That's a result of crossing your two lights. If the shadows from the two lights cross each other there's no light except what might be spilled and bounce off ceilings or walls and dark voids will appear.
When you've got more than one person in a photo with faces pointed opposite directions its difficult to get a flattering pattern with a key light off to one side or the other. A better strategy for lighting groups of 2 or more people is to cross the lights, but do it vertically. That way the shadow from the key light falls down under the nose and its downward direction naturally models the features of the face. Put your key light up above the camera and the fill light just below it and you'll have what in the generic sense is called "butterfly" lighting: named for the butterfly shaped shadow created under the nose.
That's the type of lighting set-up I used for the set of photos I just shot of my neighbor's kids: LINK It allows plenty of freedom of movement while keeping the face and body in nicely flattering light. Try it and compare with your results.
Putting a reflector on the shadow side creates the same cross-shadow lighting and unfilled dead spots as two lights opposing each other. It also over illuminates the side of the face making the shadow on the front of the face, especially the nose, darker and more distracting relative two the side of the face. You get a bright side, dark nose, bright side pattern which makes the nose the darkest shadow on the face.
Fill needs to be on the FRONT of the face not the side of the head. Reflectors work better outdoors because outdoors there is light from every direction in the sky to bounce and they can be easily positioned forward of the face. But doing that effectively with a single artificial light source and reflector is very difficult because its nearly impossible to get the reflector far enough forward to catch the light and bounce it into the front of the face where it is needed for flattering lighting.
That's not to say a reflector can't be used effectively, but for a beginner trying to figure out cause and effect of key and fill -- especially from the baseline of crossed lighting -- two lights in a key, neutral fill configuration would actually be simpler.
Indoors its actually simpler to use two lights if you simply parking one of them above the camera to serve as shadowless "neutral" fill in the same way the sky provides fill outdoors. Fill over the camera puts the nose closest to the fill source which makes the nose shadow the lightest and least distracting on the face rather than the darkest and most distracting and it reaches every nook and cranny the camera sees. The camera is usually pointing at the front of the face not the side of the head so that's where the fill is needed. That's just common sense.
Because you don't need to screw around with the fill constantly like you would with a reflector it actually eliminates fill as a variable, allowing a beginner to better understand how the key light is modeling the face. That's also a common sense approach to learning how to use the tools.
Once its clearly understood what the key light is doing with "neutral" shadowless fill there is plenty of time to experiment with various other fill positions. For example, set up a short-lit view of a face with neutral fill and then without changing pose or key light just move the fill light around to the shadow side in an arc and observer how it changes the lighting pattern. When it gets back behind the tip of the nose the fill will start to cast shadows on the face and where those shadows cross the shadows of the key light there will be dark voids and two-tone shadows. That's the pitfall of crossed light sources, even when one of the sources is a reflector.
The ideal, best of both worlds, approach is to use neutral fill over the camera to do the "heavy" lifting of the shadows overall, evenly across the entire face. Then if you want to add subtle modeling on the shadow side place a reflector there. Because the fill light is pointing at the face doing most of the work the reflector can be used with finer precision. There's also more freedom for positioning it because light from the fill or key light can by used as the source of the bounced light.
Try all three approaches and compare the results. There's no right or wrong approach, just cause and effect. There are situations where all three can be used effectively depending on the mood you want the lighting to convey. I used crossed lighting when I want to make a person look mean, tired, haggard, etc. The opposite side of the cause and effect coin from happy and flattering
And a black background and also a white background that i can use, i am going to be looking for some more paper backdrops as the colors I do have are limited. I noticed the blue was hard to shoot with, especially with one kid having a bright yellow shirt...
The following is written in a good humor, friendly tone of voice, and with the sole intent (goal) to help the original poster (and others) with a different POV.
Chuck wrote (snip):
"Putting a reflector on the shadow side creates the same cross-shadow lighting and unfilled dead spots as two lights opposing each other. It also over illuminates the side of the face.."
My Response: "Not if you know or learn how to use the tools."
Having "Flash over the camera for fill" can just as easily "flatten the light" on the face creating very unappealing and very "dull" photos.
FYI: When I say "reflector" I usually DON'T recommend using a gold or silver foil reflector. I DO recommend (general use) a large piece of white foamcor.
The "Tools" which need to be grasped are "Key" and "Fill" lights. What the source of key and fill light is, light vs reflector, is less critical to success than learning to place both most effectively. I just think its easier for a beginner to deal with only one of those variables - the key light - to start. Using a second light over the camera for fill, and not moving it, makes fill a constant, not a variable, which makes it easier to see exactly what changes to the key light position and intensity create. It's simply basic process control: you first eliminate as many variables as possible so its easier to see and control the ones that do change.
Process control also uses baselines as starting points. If you start with neutral fill and quickly gain competence creating natural modeling with the key light, from that baseline its easier to see how different fill positions will affect results. Again its changing one variable: the pose and key light position would remain constant as fill is moved around to the side, with the resulting photos taken at various positions revealing exactly what the each position of fill produces.
My advice is based on the goal of learning to use the tool - light - in easiest to understand way. Once someone does both exercises with two lights and sees understands the effects of various key and fill light placements with two completely controllable light sources, then the person will also know how to create the same effects, and what pitfalls to avoid, when using one light and a reflector.
Also consider the context - the OP's frame of reference now is crossed lighting. He obvious thought that was an effective approach with two lights, and I'm just suggesting he try a different two light approch. I also suggested he try ALL approaches and that none are good or bad, they just produce different modeling of a face with will evoke different reactions in the mind of the viewer. That's the bigger picture that beginners don't often grasp that is the keystone of my approach to teaching: never lose sight of what the goals are perceptually in terms of the desired mood and message of the photo.
I'm very comfortable and competent with both approaches I learned portraiture from Monte Zucker with window light and a reflector. At the time it was all he used for his formal wedding portraits using a set-up like this:
The subject was posed to the light of the window and the background held on a single stand in the middle was rotated around the subject as the camera position changed to capture short-lit full, oblique and profile views. Really simple, but the source for the light hitting the reflector was a big window and it was always kept forward of the face to put fill on the front of the face and avoid "spotlighting" the side of the head and shadow side ear which will "pop" out of the shadows and distract when a reflector is put too far to the side.
At the same time I was learning portraits by window light I was also learning to create the same style of 3D modeling with a pair of direct flashes at the wedding receptions. The same goal, making flattering photos of faces, but with about as different a set of tools as you could find. We used a flash on a bracket over the camera for fill, and a single off camera flash. The illusion of shape and softness was created with direct flash by learning to precisely position the key light so it didn't create an odd shaped distracting nose shadow, and modulating the fill to dial in the amount of "softness" desired in the 3D modeling of the faces: more fill for a softer look for kids and women, less for men and older boys.
Yes, too much fill can create flat lighting, but there is little chance of there being too much fill if you simply place it over the camera to start and turn it on, then adjust the overlapping key light to create brighter highlights. The concept of keeping fill constant underlies the lighting ratio convention and why the ratios use the constant of "1" for fill to describe lighting ratio: the difference in apparent brightness in shadow and highlight areas on the front of the face, not front of the face and side of the head.
The portrait ratio convention is based on the assumption key overlaps fill which is the same on both sides of the face (i.e. neutral and coming from the direction of the camera:
H:S
1:1 one unit of fill from the direction of the camera on both sides of face'
1:0 the same incident intensity of key light overlaps the even fill
===
2:1 creating a lighting pattern in which the highlights reflect 2x more light, a 2:1 Highlight:Shadow ratio as perceived in the final photo (not based on the relative strength of the light)
When the key light is raised so its incident intensity where it hits the face is 2x (1-stop) greater than fill the result is highlights which are 3x brighter than the shadows on the front of the face:
H:S
1:1 one unit of fill from the direction of the camera on both sides of face'
2:0 incident intensity of key light 2x brighter than fill overlaps the even fill
===
3:1 creating a lighting pattern in which the highlights reflect 3x more light, a 3:1 Highlight:Shadow ratio as perceived in the final photo (not based on the relative strength of the light)
So in that respect using two lights in a neutral fill / key light configuration is a significant aid to understanding light ratios and what the numbers actually are supposed to represent per the convention which is based on the difference in intensity the eye perceives on the front of the face.