fit (someone) in (to a schedule)
Is this phrase useful for scheduling meetings and appointments. When you're talking to someone with a busy schedule, you may have to ask them to "fit you in". "Fitting you in" means fitting you into their schedule. You can imagine a schedule book with each meeting or appointment taking up a block of time. If the person has enough room to add your appointment between two other appointments, then you say that they could "fit you in".
I guess it's an idiom, but it doesn't seem as though this is the best way to ask for someone to "pencil you in."