RISE: Could a current FP7-funded consortium (e.g. funded under the FP7 ICT programme) apply for RISE to increase the level of cooperation in the consortium? Or would this be “double-funding”? Would it be OK for a sub-set of the consortium partners to apply?

There is no legal provision preventing beneficiaries participating in other EU projects to also participate in RISE (as a sub-set or not that's irrelevant) provided that:
a. The beneficiaries have the necessary operational capacity to carry out the work in both projects;
b. The same activity is not funded twice by the EU budget (e.g. same networking activity, same activity funded through the secondments in RISE and trough other projects by other means, etc…). However, this is a case by case analysis.
(answer provided by REA)