Or, for an Asian example, like trying to visit Singapore, KL, Penang, Bangkok, Angkor, Phnom Penh and Saigon in 7 days.

I'd say, do London, Paris, Brussels and Amsterdam, and take trains between them (it's early enough that you can still probably find decent fares for Eurostar and Thalys high speed trains, see eurostar.com and thalys.com). Maybe add Cologne if you really want to cram things in.