Games : Playing online with two PS3s having the same PSN

I have two PS3s with the same PSN account. Given from the information released by Sony with one PSN account I can have up to two PS3s and one PS4. But whenever I sign in to PSN from the second PS3 the first is signed out. Is there a way to have them both online simulteanously? I found another answer here that suggests no but it was never accepted nor highly upvoted to denote that it is the only answer with no alternatives. What if I activate both consoles as my own? Would that make any difference?

If I cannot do so (have both online with the same PSN), does that apply if the accounts are on different versions of a console? (For example one is logged in with PS3 and the other PS4 or PSVita)