Would it hurt my career to go from COCOM to COCOM?

It is absolutely critical to get tactical time if you want to stay in the military. Not just for the broadening, but for your own development and time with Soldiers. You aren't leading much at the COCOM or ASCC level. As a SSG you should be around Soldiers and training and leading them.

Also take a look at promotion board precepts over the past few years and get a handle on how they look at it. My experience sitting on boards is dated but I lived through the dark years of "joint is death" to "joint shall not be disadvantaged". The issue I've seen more of is similar tours can result in a gap in something else that makes up the desired pedigree. If there are 5-6 must do things, don't delay getting them punched as Cpt Murphy's Law will intervene if you work it too fine. Also consider if you'll lose touch with the important things of your MOS, i.e. hands on doing real things in the real world with your troops.

Think about the kind of paper you'll get from the second tour. About all you can get from a COCOM is "he's a great staff wonk". What you can get elsewhere is paper that directly talks about the contribution you made to primary mission success. That's the difference the "shall not be disadvantaged" piece was supposed to overcome but that only goes so far. Boards not only look at what you've done, they try to project what you'll do down the road and will you likely succeed. Silence on critical contributions and leadership stretches the betting odds, hence a dangerous place to be if you're in the third crunch.

BTW, I had 5 years with PACOM but made sure I had two lives. I was 7th Fleet Engineer a part of it and then shifted to State and USAID work in SE Asia, mostly in Cambodia. So you can get "operational" paper if you're able to get out in the real world.

I don't think that it would hurt your career, but I will say that senior boards look closely at variety of assignments. It is to your advantage to seek out new challenges. But if you feel that you have found a niche where you excel, by all means do another tour at a COCOM.