Full disclosure: I'm asking this as a displacement activity while I should be reviewing a paper.
Given how well journal clubs etc work, it has occurred to me a few times that reviewing a manuscript as a group would probably result in faster turnaround and more detailed comments. However, typically journals approach individual reviewers and place confidentiality restrictions on the reviewer so this mechanism wouldn't work. Does anyone know of any journals, ideally in the life sciences, which support or even encourage collaborative peer review of manuscripts?
Most of the European Geosciences Union (EGU)/Copernicus journals do something sort of like this - they've been doing it for some years and it mostly works out well. The journals are fairly reputable in their fields and from what I can see authors seem to like them.
EGU describe them as "two-stage journals with public peer-review and interactive public discussions".
Unhelpfully for you, though, these are all geosciences. (List)
The process is:
posted as discussion paper after initial approval by an editor
reviews & responses posted publicly, with third parties able to post uninvited reviews
The system still works on individual not collective reviews, but the fact that they're public potentially allows them to build on issues raised by each other, and I can't see an obvious reason they wouldn't accept a review contributed by a group.