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I guess one solution would be to put the request on hold and serve it as soon as enough slots are open. Or isn't this a problem?

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This isn't acceptable unfortunately. VMs are meant to run for quite a reasonable amount of time, so we'll be waiting very-very long until slots get available...

OK, so we just reject those demands?

We can't reject as it'll be used in the commercial application with users paying money for using cloud resources.

Basically what is needed is to find the list of VM migrations needed to be done to free enough space for a new VM (of course, if it's ever possible).

Yes, my question was: What to do when it's not possible? Put it on hold or reject it or automatically buy new servers?

Yes, completely reject if it's not possible at all.

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