"a mouth full of wirenuts "
Ahh, now I understand why they come in different colors ... they're different flavors! Thanks!
OK, now, for the real post:
Your local laws would determine the details. Here's how it works in Nevada:
A company must have a 'business qualified' person, as well as a 'trade qualified' person for each license. One person is very often considered 'qualified' in both business and one trade, but it starts getting tricky for one person to qualify for more than one trade.
You see, the 'trade qualified' person has to document five years of work at journeyman level. In addition to this period, circumstances also conspire to make this in additional to completing a several-year long apprenticeship program. Therefore, it's pretty hard for one person to be 'qualified' in more than one trade.
So, your proposed company would, by Nevada rules, need at least three 'qualified persons' in order to hold the necessary licenses. Should any of those people leave, you have a very, very short period in which to come up with another 'qualified person.' Essentially, that person has to already be on board, and ready to begin the application / testing process right then.
That's another devil in the details; there's essentially no way for a person to become 'qualified' in advance. If you were in the middle of a project, and (for example) your guy holding the 'general' license were to get hit by drunken alien who wandered away from Area 51, your company is going to be hurting.
I think you can see that this sort of arrangement has some special concerns, that will have to be addressed in the way you organize the company.