Piggybacking arts organizations?

According to the Chicago Tribune, New York isn't the only theatre scene with space issues.

Depressing? yah.

What interested me was the mention of the Children's Theatre that is piggybacking on a museum for their space. It didn't seem to be an ideal situation for them and I'm obviously not a fly on the wall at their board meetings, but I wonder why these organizations are working against each other?

Which makes me wonder: in hard economic times, is there a place in New York for larger non-theatre institutions to develop collaborative fellowships to emerging artists from different mediums that deal with the same issues? How much would you benefit from being able to develop and present a multimedia ensemble piece with the Museum of Photography, for example? Does this already exist somewhere?