Some schools have alternate dates (like a one day visit) or will skype you, or otherwise let you switch your date. Don't worry...this is a good problem to have and if they don't want to accommodate you they don't want you enough! That said prioritize and be prepared.
Some of them have you book directly through a travel agent! Of my 2 invites, one has you do reimbursement, the other asks you to contact their agent if you plan on flying/taking a train
I emailed the PiN (was asking because I'm worried about potential conflicts) and they said if you don't hear by the 21st, you unfortunately aren't invited for an interview