Thank you for trusting your question to JA today. I am a licensed attorney with over a decade of law practice and over 20 years of experience in the legal field. I’m happy to be of assistance.
We are asked this question on a regular basis, but there isn't any loop hole to allow separation AND allow you to be eligible for other branches of service. In fact, just getting out of the service is near impossible now, unless you're willing to break the law (and guarantee no chance of getting into any other branch).
After nearly three decades of constant deployment across all the branches, all the old loop holes have been closed. Homosexuality no longer works. Gaining weight and/or failing PT tests might work, but it would keep you out of other branches due to the negative RE code. Claiming conscientious objector status would do the same (if it even worked...as usually they just transfer you to non-combat/support).
Family hardship situations might be able to be claimed (if you were taking care of a sick family member that had to have your support), and then following that person's rehabilitation or death, the thing that caused you to be separated would no longer be accurate. You could then seek a waiver to allow separation or file a DD Form 149 to change your RE code, but you'd have to have those personal facts for it to work. You'd need affidavits and medical records to establish the issue.
Any other method of separation is going to hamstring your ability to get back in (medical, mental, PT failure, drug use, alcohol, failing advancement tests, conscientious objector, etc.)
The only way to get out and preserve your ability to rejoin another branch is your regular ETS date.
If you have any further questions, please let me know. I invite follow up questions, so use REPLY for those. If you have no further questions then good luck going forward and please do not forget to rate my service with a three, a four or preferably a five star rating so that I receive credit for working with you today. Please rate me based on my service and not on your satisfaction with the law, which I am not in control of and I am just reporting to you. Also, feel free to request me in the future, if you have questions concerning a different matter.