Is it safe to take vita liver to help process fat better when CoolSculpting?

I have been researching CoolSculpting and reading a lot about how the liver helps destroy the dead fat cells. I have read multiple times how you shouldn’t take an anti inflammatory. I was researching how to make you liver process things better and there is a supplement called vita liver which contains milk thistle, artichoke, dandelion, etc. All help the liver process things better but also have anti inflammatory effects. In theory it should help more than hurt, thoughts?