At the distance you'd be away from a group of 20 people, any normal 4' umbrella or light box is going to take on the characteristics of a point source, no diffusion can soften it. Even a jumbo 6' one might as well be a shoe mount flash in the way it renders.
Think about a (good) car photographer in the studio (if any still exist?) they need to use a giant light box at least as large as the car itself, and then position it as close to the car as possible. Same physics are in play with a simple studio portrait... get the light close to the subject. This makes 10x more difference than whatever corny store bought modifier people use.... as if a shoe mount flash with a gizmo over it is going to somehow be "softer" when shot from 20' away. LOL it just doesn't work that way. Same idea as people taking photos at concerts and sports events from high up in the stands but still using their camera flash.
One you get further away all the modifier does is rob you of light. You're much better off taking all the modifiers off and aiming the light directly at your group. At this point all hope is lost for those wearing glasses, who are bald, or have extra chins. Just get the shot. You're probably going to need all the power you can get since you need to stop down to get everyone in focus. Try to get smiles and it's good enough.
I don't know what you have for a light source but if you have a lot of extra power then yes, bouncing off a large white wall can be a lifesaver. But we're talking an AC strobe, not a shoe mount flash. Watch for color shifts from the reflective surface but most of the time it's correctable in post.
Personally, being lazy and preferring the natural, I try to get people outside into open shade or pray for overcast. I don't bring lights but I do bring a step ladder so I can get over them and try to find ways of separating their heads from the backgrounds by picking the height and backgrounds to minimize overlapping people. Imagine the challenge of dark hair, dark suits, and a mix of pale and dark skin....
When I had to do it for corporate work I would "build" a nest of multiple strobes and umbrellas just off frame, as high as possible, art 45 degrees. With some set-ups I'd use a second light at quarter power to the opposite side just to fill. But you do a lot better finding physical help with fill and separation, like using a large white wall instead. When I had to I'd cheat it towards the camera if I wasn't able to build the set I really wanted. Shooting light straight into their faces isn't as pretty but if you don't have enough light then it's the most efficient use of light.
Getting them drunk is another favorite technique!
(Examples are ancient and not without fault. The industrial one is just the kind of survival mode shot you often are forced into, in this case I think I used two of the largest lights up high and aimed down at the subjects hoping to throw shadows onto the floor while I stood high and made them look up at the camera so light hit their faces. Given the time and circumstances it's OK and everyone was happy with the non-birdie shot. The now green wedding (old color profile) was simply the perfect hazy overcast daylight, so much better.)
I quit doing this junk back in the film era but nowadays I think you could take a modern DSLR, powerful shoe mount flash without modifier and pointed right at the center, and stand on a ladder to make people look up at you. ISO 1600 and f/6.3 on a 35mm lens would probably get the job done, allowing for a little Photoshop post.