Great ideas!
I've had frustrations with apartments in Europe because they often want a minimum stay of 5 days to a week. We often go away for weekends so it usually doesn't work for us. Doesn't mean it's not an option or that anyone reading shouldn't try!
I like the hooking up with another family idea. This might work for us in the future (so far no but they're older) but I wouldn't put kids alone in a room unless it's connecting with at least one of the other two rooms. Some hotels don't allow under 18's in their own room. You can cheat by booking one of the adults in it. Fudging on this one would be a real judgement call!
Another version of this idea would involve getting a suite and a separate room and then spilt along whatever lines worked for the whole group.
I found that usually we were allowed a crib in a double room when our youngest was still in one. It was usually allowed so chances are, even if you didn't mention it, it might still have been okay.
On a general note, remember that beds can be a lot smaller in Europe. When making out your battle plans, keep this in mind. Contact the hotel if necessary and ask about sizes. I honestly can't share anything less than a King with my dh. When we've had to do doubles, we have to put an adult and a child in each bed. Probably why we don't have a 4th too
If you are visiting friends/family, many can't or won't host such a large gang. Depending entirely on circumstances and relationships, one other option has been to send one parent with one or two children to the relatives and then just getting a standard hotel room for the other parent with other child/ren. Another version is to have children stay with similar aged friends or cousins. Families might be more willing to host a kid or two, and make it a sleepover, than to have adults with multiple children in their house.
We do this in Paris, a city with tiny hotel rooms and my dh suffers with the tiny hotel beds. His elderly uncle wasn't thrilled to have noisy small children in his house but could deal with just my quiet boy, who then gets a break from his two baby sisters. I used to live in Paris, so I actually prefer to stay in the center, see friends and shop rather than be stuck out in the suburbs the whole time. We have the car so my dh plays taxi and otherwise, I'm know the Metro well.
Definitely an unromantic way to see the City of Lights but it works for us!