Yes

Had a Soldier once assigned to my unit that wore a USMC Combat Patch on his uniform from action in Somalia. IIRC you may want to look at AR 670-1 or just talk to an NCO.

If you are on detached duty with another HQs you often have the option as to which compbat patch you can wear. This is common amongst CSS folks who can get moved from unit to unit they are supporting. AR 670-1 is your best choice. However unit policy can over ride that if a commander wants everyone to wear the same patch.

If you have earned a patch and can back it up - wear it - flaunt it. I wore my gold aircraft spotter badge on my airforce "uniform". Any questions and a long Clint Eastwood glare just made whither. If you wear another badge to look smart - you are pathetic. A uniform is a merit statement - not a fashion statement!

I also was deployed to IRAQ. HQDA put out a memo starting in 2007-2008 that a sm will only be authorized his lowest level unit patch. I was in baghdad and also should have been awarded the MNFI patch but because of this memo was not. I was deployed with my cousin who was put on a detail for a MG his entire deployment he received a memo form said MG and still cannot wear the patch. I recently moved units and all the soldiers of that unit had to take off their combat patch becaues it was not their "unit" patch. so in other words if its not the patch you deployed with on your left sleeve then its not the patch you can wear on your right sleeve.