First off, let me start by saying that the Big East should stick to basketball.
Secondly, let me report that it was recently leaked to ESPN that four schools have been extended invites to the Big East. The conference in flux made offers to UCF in all sports, and to Boise State, Navy, and Air Force in football only.
And in my mind, every one of those four schools is a bad fit.
Let's start out with Boise State and Air Force.
Boise State probably deserves to be in a BCS Conference. However, I would recommend that they hold out for an invitation from the Big 12 rather than the Big East. It makes more geographic sense and the Big 12 has the high-caliber schools which beating up on will get you a spot in the BCS Championship Game.
Boise State and Air Force have no tradition whatsoever with any of the current Big East schools, or any of the new potential Big East members (save Navy). They don't even have tradition with each other.
And consider the culture of the Big East. Most of the Big East schools are Catholic and/or in big cities with traditional Catholic populations and student bodies.
Not only are Boise State and Air Force over a thousand miles away from Louisville (the closest Big East opponent), they don't fit that profile. They're in small-to-medium-sized markets that are among the LEAST Catholic in the nation. Boise State, a former normal school, in addition doesn't fit the academic profile of most of the current Big East schools.
And what are Boise State and Air Force going to do for basketball? Stay in the Mountain West? Work out a deal to be in the Big East for football and the WAC for basketball? Go to a basketball-only conference like the West Coast, Missouri Valley or Big West (the latter being a return for Boise State)? Go independent? They haven't really thought through that logistic.
Navy is one of only two schools to have never been anything but an independent (Notre Dame is the other). Call me a bow-tied iconoclast, but I want to keep the tradition of Midshipmen independent football alive. Joining the Big East would endanger its longtime rivalries with Notre Dame and Maryland, assuming that the game with Army remains intact. Now, if you were to get Army and Notre Dame (both of whom I do think would make a modicum of sense in the Big East) to join Navy in the Big East, it would make some sense. Just Navy, eh, not so much.
Central Florida is the only one of the four to be invited in both football and basketball. It, like South Florida, is a large commuter school in Florida without much tradition. Though UCF makes sense because of the "I-4" rivalry with USF, it doesn't make sense in that UCF and USF are much different from the Big East profile I outlined above, to say nothing of being geographically distant. UCF in basketball doesn't make any sense at all to me...UCF has a much shot of being competitive in Big East basketball as a man has of survival when being surrounded by five sharks, six lions and a piranha.
A further reason that none of these schools should join the Big East is that the Big East won't be terribly relevant even with them in it. The Big East risks the danger of becoming an irrelevant mid-major conference (it hasn't been to a BCS Championship Game since 2001; its last conference champion wasn't even ranked in all the polls), and it would likely be shut out of a superconference playoff.
Call me sentimental, but I don't think the Big East is the right fit for any of these four. That's the bottom line.