I want to become a creative commons record label that publishes music with PRS but licenses them under CC by SA 4.0? Is this possible?
IANAL/IANYL, but mostly, as I read it, it is not possible. When you join the PRS as a writer, you agree to their standard terms of assignment for writers, which amongst other things say:
[2a] you transfer to us absolutely for all parts of the world the rights which belong to you on the date of this Agreement or which you may acquire or own whilst you remain our member
[4c5] you promise to refrain from licensing any of the rights and from otherwise dealing with rights which you have transferred to us
The limited case I can see that would work is if you published your work under CC BY-SA, then joined the PRS and assigned this work to them. Since free licences are generally irrevocable, anyone who had already got a copy of the work under those terms would retain their rights, including that of sharing under the same licence terms. But you would have undertaken not to publish it to any more people under those terms when you assigned it to the PRS - indeed, you would no longer have the rights in order to so license them - so you would have to stop distributing it under CC terms.
This isn't crazy. The PRS exists to centrally collect and distribute licensing fees, that is to say payments that need to be made in order for third parties to secure a copyright licence to perform or physically copy music. But if this music is licensed under CC BY-SA, everyone already has those rights (subject to certain accompanying obligations), and there is no additional need for a payment to secure them.