On Linux an idle instance of multichaind will take about 0.15% of a CPU core (measured on a 2.4 GHz Xeon) and 40 MB of RAM. So if you get yourself an 16-core server with say 512 GB of RAM, in theory it can run 10000 instances of MultiChain.
Of course I'm sure it won't work out quite so well in reality - because your instances won't be idle, and because there will be some contention over memory and disk access. Nonetheless it's not a completely crazy prospect, and I can only recommend that you run some tests to see what you can do.