It sounds like the suggestion "it should be possible to scale websites individually, even when they are in same region" is spot on regarding this issue. The idea is "under review" as of Dec 23, 2013, so the current answer is that no, it isn't possible yet.
Update: Closed (WONTFIX) as of March 20, 2014, though apparently based on a misunderstanding or simply incorrect information (see comment on the suggestion thread). There's still a chance they might reopen when they realize this (or when the issue pops up again in the future), though I wouldn't rely on this assumption.
Thanks BrentDaCodeMonkey for clarifying that sites are grouped to run on sets of instances within regions / data centers as opposed to just by subscription. I guess a "work-around" would be to isolate sites in different data centers, though it's likely that it may be more cumbersome than anything in many cases.
Update: Feature announced on April 4, 2014.