Like so much in the nonprofit world, there is no single answer that works for all situations — unless you adopt the lawyer’s approach that “it depends.”

In general, it is probably not a good idea to have a single person serve as president of two separate and independent nonprofits, particularly if the person is otherwise employed full time.  It usually requires a significant time commitment to do all of the things required to serve well as the president of a nonprofit board.  If your current president isn’t doing what you need, you should talk with her to see if she can change her ways or if she is willing to step down.  If you don’t get the result you want, you undoubtedly have the right under your bylaws and the state nonprofit corporation law to remove her from office.

If you are dealing with someone who is not otherwise employed full time, a person may have more than enough available time to do both jobs well and, assuming that the two agencies are not in competition, could lead both of them effectively.  The person may or may not do it well, but there is no inherent impediment. 

If you are dealing with subsidiaries of a single parent organization, like a healthcare system or social service agency group, having a single person serve as president of the subsidiaries may be the most efficient method for administering the plan and policies that the parent organization sets for the entire system.  So, as I said, there is no single answer — other than “it depends.”