Here's an interesting idea that's currently being proposed in the EU:
Although who this would be useful to would depend on how much the annual fee was.An associate membership could provide all the rights of full European citizenship, for example the right to freedom of movement, access to healthcare in the EU and the right to reside in EU member states. Following the reciprocal principle of “no taxation without representation”, these associate citizens would pay some form of annual membership fee directly into the EU budget. In return, EU associate citizens would be able to stand and vote in European elections via trans-national European lists, which we hope will replace the vacant seats of the 73 British MEPs who will be departing in 2019.
I have no doubt it would have been better for the UK to stay with us in the European Union. But if Brexit means Brexit, then I see no reason why the EU should not, in principle, offer an individual EU associate citizenship to UK citizens who wish to maintain their European identity.