Including an interaction variable which doesn't vary within a key control variable

Question

Let’s say we want to check the effect of the interaction of education level and gender of the salesperson on number of units sold by them. We have thousands of sales people in the data, but they only come from 10 companies: 4 of them hire (almost) only men, 4 hire almost only women, and 2 companies hire both men and women (let's say the employees are independent of one another). We want to control for the company, but that pretty much kills any variation in the gender. Is there a way to still rule out the effect of the company? If the gender is really important for the research, is there a good way to check whether the company doesn’t matter much? How would you go about it?