Closing - Multiple C level exec interviews

I am a Chief Information Officer with experience in healthcare in transition.

I've been interviewing during the past few weeks, at a number of similar organizations, and have been scheduled through retained and contingency  recruiters.

Since the position is a senior management level, reporting to either the CEO or COO/CAO, I have been scheduled fo multiple interviews over multiple day/weeks at each organization.

Is it appropriate to close at each interview, knowing I will be back later that day or future days/weeks with other executives before they convene and discuss the various candidates?  It seems a bit odd to me to close with the first of 3-4 interviews in this format.

Any advice?

Mark / Mike - great job with Manager Tools - I have put your advice to work many a time and look forward to each new episode.