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

BLUF; Yes. Not concurrently however. Once you complete your mandated (contracted) AD period and returned to Reserve status,you can apply for enlistment into a second branches. The recruiter for the branc your applying for has the guidelines on how to get you released from the branch you are leaving. Depending on the new branch you select however, you may need to attend that branches Initial Entry Training

Multitasking:-)Interesting !!!

I think as long as you qualify you can serve in any branch. My best friend served in the Marines, Navy Reserve and finally the Army. However, if you want to make a career of the military, I suggest that you stick to one branch and ride out a 40 year career.

Don't get ahead of yourself, figure out if you love what you do (it sometimes takes a while) and then go from there.

Yes! I had a friend who Served in 4 Branches. He started in the Navy, went into the Marine Corps, Army and finished in the Air Force. Just as long as you finished your enlistment.

Everyone has posted good advice, one thing that comes to mind is that it seems to me that the people I have known that have been in multiple branches promote slower. As with anything, some people do bust on through and promote fast anyway
I would agree that whichever branch you choose, stay with it.
Retrain and learn a new skill. The closer you are to your final date of separation (hopefully retirement), try to find a job that translates well to the outside world. Medical is one of the really good crossovers. IT has been good for people also.
Being a highly trained killer is always exciting, and a adrenaline rush, but the matching job pool is just a little small on the outside ;)
Good luck, make it fun !!

Of course. Hell, in today's military you can be two different sexes while in only one branch. The sky's the limit.

My Dad served in the Navy in WWII, and the Army during Korea....

I was in the Navy from 85-89, the Marines from 90-94, and the Coast Guard from 99-2012. The Navy wasn’t a good fit, I liked the Marine’s but I was home much to raise my children. I retired from the CG, it worked out well for me. The draw backs are starting over and learning all the particulars of the branch you’re in.

I have served in 2 branches. I served 6 years in the Active Army, 3 years in the National Guard, and then 3 more years in the USNavy Reserves, attached to the USMC. Before I changed, I did full tours in each branch. I was able to utilize the skills I had from each time in to enhance my value and knowledge. I learned new and different skills from each branch that increased my respect and comradeship for ALL of my extended family. The one thing I do regret is that when you cross over in services, you lose one to two ranks, having to "start over" going up the "rank ladder". If you're willing to go thru the training to an extent...again...go for it. But remember, that your first enlistment will make the most lasting impact on your military...and civilian life. You'll get used to doing things a certain way, and a change in branches can be a type of "culture shock". It's exciting to try and do new things, just be aware of all the aspects before you make your decision.