Can we expand and branch off with a 501 c 3

Not enough info, what type of 501C3 do you have, what is its purpose?

What do you plan to branch off with. I mean a church will do a food pantry, a thrift store and perhaps a homeless meal kitchen. They may do a kids program and so on.

Is the new branch related to the main goals ?

My friend has a 501c3 that is for kids, they started with a martial arts program, they now do dance programs, and computer programs all for kids.