In Florida, you may qualify a company and then with board approval, appoint a financially responsible officer who the assumes the responsibility for all financial matters.
Chapter 489, Part 1, Florida Statues:
489.1195 (c)
"Where a business organization has a certified or registered financially responsible officer, the primary qualifying agent shall be responsible for all construction activities of the business organization, both in general and for each specific job."
That being said, if you work out a deal with your suitor, and are sure that you are protected, there isn't any reason not to go for it.
Here in Florida, there are quite a few people that qualify multiple companies.
You must appear before the board, explain why you are doing it , and how you are going to control multiple businesses.
I know of one well respected code instructor who qualifies multiple companies in the electrical trade as well as a general contractor, pool contractor, and shutter company. This is his job and he keeps track of all the companies on a day to day basis.
I did it several years ago in another state and it worked quite nicely for me.
A company that did specialized fire alarms in power plants came to town and needed a license for two jobs.
I became a non voting officer of their company and they paid me quite handsomely for my participation.
I had an office on the jobsite and was able to inspect the installations any time I cared to.
I was present at all inspections as well as during systems testing.
Just make sure that you have an attorney who is familiar with the business laws of your state who will write the agreement and you should be fine.