Is it possible to be signed up to a publisher but to also self publish? I am currently working with a publisher but in the future I would quite like to write a book series and the publishers do not have that option.
Most publishers will require exclusive rights within some market before they'll buy your book. That means you won't be able to self-publish the same work until after some period of time, when your contract with the publisher expires and you "get your rights back" to your work.
You'd want to have your (proposed?) publisher contract checked by a lawyer experienced in contract law to be sure, but there would normally be no prohibition against publishing other works by other means -- either through another publisher, or via self-publishing.
Everything depends on the details of the contract between publisher and author. It is not uncommon for legitimate major publishers to demand an option on the author's next work, I understand. The exact terms vary. It is far less usual to demand an exclusive deal, and that feels abusive, but such a contract would be possible and might well be legal, even advantageous in some circumstances. The next-book option is most likely to be limited to the same general field or genre. Lewis Carroll's publishers would not have demanded an option on his next math text, for example. (Actually Carroll self-published, but he makes a good example). But there is no absolute rule, publisher and author may contract as they please, or more realistically publisher may offer whatever terms it pleases and the author can accept or not.