Some chapters do extend bids. It's not something I'm in favor of (and neither is your chapter), but it does work for one chapter I know of in the midwest. Their "cap" is very high though, so not that many people get rejected.
To reduce your size if it's indeed becoming a big problem:
You could have a pledge class in the fall, then opt out of a spring pledge class. (I think a chapter in my region does this)
You could have an "open rush" in the fall and a "closed rush" in the spring -- by that I mean you still have a spring pledge class, but you don't advertise for it and pretty much rely on word of mouth. (Though I imagine with 200 brothers, word of mouth would be just as successful lol)
All things considered though -- this is a wonderful problem to have. It's great to hear that so many people are interested in your chapter!
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