@gollum,
It depends on your donor's wishes and also on your mission. If one of your missions is to support other like-agencies, then, yes, you can make a donation to other groups. They don't even have to be a 501(c)3.
I don't know about a "fee" for doing this. You take $$ in and disperse it.
You may have administrative costs. You would not call that a "fee" but rather it would be part of the program.