Not sure about any groups, but I'm not on any mood stabilizers (in the sense I take medications categorized as mood stabilizers) because I don't respond well to them or antipsychotics.
I take topiramate, an anticonvulsant, sertraline (Zoloft) and I have a prescription for clonazepam that I rarely touch. I also have temazepam 30mg I take sometimes because I have severe insomnia and have for years. Also, not for my bipolar disorder (I'm diagnosed with bipolar Ⅰ — severe, recurrent, ultra rapid cycling, most recent episode manic [I know this because I'm having to apply for SSDI/RSDI or I lose state healthcare and I have a copy of a state psychiatric evaluation from April]) but I'm on dextroamphetamine 60mg total daily, I'm allowed to divide the doses as I see fit for each day as long as I don't take more than 2 10mg tablets in a 4 hour period.
I LOVE the topiramate, it's eliminated so many of my bipolar symptoms, it's amazing. I wish more doctors would give it a try. I was who brought it up to my psychiatrist after reading some studies and he basically said "why not, we don't have many more options" and that was that. (My psychiatrist listens to my input and thoughts on treatment and takes them seriously, though I don't really touch the ADHD meds, I let him suggest all of that.) The sertraline was started after a nearly 5 month period where my agoraphobia got so severe I didn't leave our apartment, not even to go down to the mailboxes to get mail. Once it got into my system and working 100% after 5-6 weeks, I was leaving and going out doing stuff without a second thought and without clonazepam.
I don't react well to any other SSRIs, though. Zoloft for some reason doesn't trigger mania or psychotic episodes like others do. It's wonderful at keeping my mood stable and happy, I'm so much more pleasant on it. My husband keeps commenting on it, especially since my recent increase from 50mg to 200mg. I also love the added benefit I get that it wipes my PMS out. All I get now are cramps. I don't get the emotional rollercoaster or anything. I can live with that. ;)
The other medications, they don't do much for the bipolar. The dextroamphetamine helps my mood, too. I'm really resistant to treatments for some reason, the usual ones just do not work.