A ”standard” round refector with a honeycomb, 2-3 of mylar and, a two way barn door attached to it... That's some standard refector Darrell!!
Let me explain 'why' a standard reflector, diffusion materials, a honeycomb grid, and a barn door set should be in EVERY single studio lighting kit.:
A grid is a wonderful tool. A grid keeps light going "straight ahead", mostly, and prevents the spread of light. A gridded softbox can be used close to a subject, and because the box has a grid on it, the softbox will light pretty much just the subject, and the light will not spread, and will not reach to even a pretty close-in background wall or background paper. A grid, in effect, causes a rapid fall-off in the light's intensity. There was a time in the 1980's when egg-crate type softbox grids were "new", and it was fashionable to place a person in front of a gelled, colored backdrop, and then to light them with a grid, so that the background stayed dark (meaning the backdrop was NOT lighted by the softbox), and that kept a gel color from being "washed out" by extraneous light hitting the backdrop; extraneous light from the main light maintained the color saturation of the colored, gelled light that was coming from a backdrop light unit that was providing said gelled light. This effect still looks good to me.
But back to the standard, metal flash reflector bowl. A grid on a standard reflector, like a 5- to 8-inch (or even a 10,11.5,or 16-inch) metal reflector from a studio strobe, works well, but the light tends to still be a slight bit raw, and hot, and when the light is angled in at the subject at shallow angles like 5 to 25 degrees from behind and angling in toward the lens, it can create a very "hot", specular highlight on the cheeks,jaws,neck,etc.. With a gridded light at a softer angle of incidence to the subject and to the lens, the light is not so "hot" and specular. The reason I like to add mylar diffuser material (think gallon milk jug in color and density, but made by Speedotron, clip-on mylar diffuser) is that it allows the light to be placed fairly close-in, so there's not a lot of spread, but it keeps the specularity of the standard reflector's light closer to the specularity level of an umbrella or a softbox.
A softbox is a soft light modifier, so if you hair-light with a grid-equipped softbox, then the light will match-up pretty well with the main light's softness. So this is why so many people use a strip box or a softbox as their hair light. The only issue is that it has no control over spread angle, and not a lot of adjustment for brightness/specularity. Those are why I prefer using
a metal reflector, 11.5 inch, with a grid ( either 10,20, or 35 degrees), and mylar diffuser(s) either 1,or 2,or even 3 diffusers, and a Two-Leaf barn door unit; this allows you to create a LOT of different lights; hair light, rim light, accent light, wide angle, medium angle, tall,skinny, narrow, whatever. You can go from hot,specular,hard light, down to pretty soft light, and can cover 50 degrees to less than 5 degrees of angle, all off of one light unit.
When you have a standard reflector, and a grid or two, and some diffusion material, you have a HUGE range of lighting capabilities. Add a barn door set, and you can light a zillion things. This is NOT the case with a softbox or a strip-box, which tend to be large, and very limited by comparison, in how their light output can be modified and controlled.