Sometimes, yes!
The best way to keep your rights is to work with a publisher that you are licensing your work to, usually through open access publishing under a creative commons license of your choice.
While some journals will allow you to do this at no cost, costs vary significantly by field, outlet, and funding model. If you are keeping your sole copyright, you will often be asked to pay for the publication costs through a publication charge. This can be $500-$2000 for an article and in the tens of thousands of dollars for a book.
Publishing in a Diamond OA journal or self-publishing your books may allow you to maintain your rights at a lower cost, or even no cost at all. We’re happy to meet to discuss your options - email us at scholarlycommunications@bucknell.edu
If you want to negotiate to keep some of your rights without paying, your best bet may be to select an Author Addendum to use in your negotiation. While you may still be transferring your copyright to the publisher, an addendum will allow you to continue to reproduce, distribute, and make derivative works from your work.