Can a PI or Co-PI apply for more than one Thought Summit per call?

No. PIs, Co-PIs (aka collaborators) can only participate in one Thought Summit per call.

What time frame does the Thought Summit need to occur?

It depends on the timing of the CFP.  If the CFP is in the spring, the Thought Summit would need to take place within the next July 1 – June 30th fiscal year.  If the CFP is in the fall, it may be able to rollover to the following fiscal year depending on funding.