Is it possible to serve in multiple branches of the military ?

I joined the navy, corpsman , served with the marines, then went army

Heinlein said it all, "Specialization is for insects".
The best advice I can give you is to seek to be a polymath, and not a dilettante.

Prior service from any branch will most likely find it hard to get into the Air Force. Spend a few years in the Army and look into a commissioning program like ROTC. All the branches have ROTC but you will have to look around for a college that has the branch of service you want. If you end up in a medical field (Doctor, Nurse) all the branches want you. Best of luck!

PFC Cinnamon Hack as a Company Commander I had several people who came from the IRR that served in the Marines before. Depending on the service you are going to, where you are coming from, and how long you have been away you may have to redo your basic training. Also, you may have to do their individual training to learn a new trade/job/MOS if they do not have the same type of job that you had before. If your goal it to switch from service to service then you should look into what job you want to do in each and what you have to do to be qualified for them. But do not look too far ahead that you are not able to focus on the here and now and be successful. Good luck.

I served 3 years in the Air Force and 17 years in the Navy. I had to go to boot camp again but it was well worth it to me.

I served 12 years in the US Navy and 15 years in the US Army with a 6 month break in service.

I suggest that you concentrate on the Army, do the very best you can do learn how to do your chosen job. Once you finish AIT go the extra mile. Study on your own, use the internet to learn more about the job you chose. Read the Commanders reading list for enlisted persons. The list is laid out for you to be a better soldier. Jumping around the services does not make you a better soldier. You will be able to add as secondary MOS later in your career.

I'm an example of crossing over. Worked 10 years in the Navy as an OS and after an 8 month break in service, enlisted in the USCG to the same rate and grade I departed the Navy from. The Coast Guard was in need of OS's so I was able to get my rank back and was sucessful in requesting the west coast. I guess the main thing to look for is do the branches of service have the same MOS your working in, if not crosstrain into a job that does.

Yes

Army Aviation to Air Force CSAR back to Army to retire.