Is it possible and architecturally wise to execute another stored
procedure from a sp?

I have currently a selectable sp with many IF statements, all of them
return a select with same fields, but with different conditions.
I am thinking to divide them into several stored procedures and have
main sp to calling out others. something like

if () then
select * from sp1

else if()then
select * from sp2
etc.

is it wise to do this way? is there a good sample for doing it?
thanks.