Can I connect my PS4 to my PS Vita if they run on different accounts?

I have a PS-vita and and a PS4 and both run on seberate accounts. I would like to connect my PS-vita to the ps4 to use the remote mode, but this is not possible because it uses a different account.

I have already tried to change the PS-vita account, but that didn't work either because I "activated" it with the account.

Is there a way to connect the devices anyway?

Remote play and connect via USB should be possible or same network.

Unfortunately, it's not that easy. Always get the message that I should log in with the same account.

But that doesn't work because I activated PS Vita with an old account…