Yup, I second CalCPASoon's reply. Within healthcare, once you understand the industry players, jargon, metrics, standards, regulations and reporting, you can jump over to the for-profit parts of healthcare as well, including pharmaceuticals, consumer and commercial health products and machinery, health services, insurance, etc.
After I graduated with my accounting degree, I did some low-key bookkeeping work for a small performing arts NFP, which I've kept on the side since. I basically use that gig, and a few other similar NFP ones, to make some extra consulting and bookkeeping money in my (very slim) spare time. While it's different from my day job (in public accounting with for-profit clients), the basic accounting principles are relatively the same. I would say that I also have more operating experience from working at these small places as well, dealing with liability and health insurance coverages, worker classification and state unemployment issues, and researching tax issues and credits.
And don't worry, I've had a pretty bumpy job history since I graduated as well, with my longest gig lasting 2 years, and maybe 4 gigs in the last 5.5 years. Sometimes it just takes a while to land some place that works for you and the place. Congrats on passing though – at least that's off your plate!