As someone with elevated cholesterol, is keto even possible while I eat only fish?

Absolutely because here's some data that you may not know. Cholesterol many times especially the kind that can invade your arteries is converted from carbs. So if you're doing the fatty fish hence you're going to be fine. Then do the rest vegetables, not the grains, not the sugar because the fatty liver can be coming from nonfat sources. It could be coming from vegan carbohydrates. And so they found that if you do a low carb diet the fat on your liver potentially can reduce to 50% in two weeks.

I would combine the healthy keto with the fish and do an intermittent fasting together. That'll be your best bet. I'd probably add into the mix the milk thistle because that's one of the best remedies for supporting liver and improving liver enzymes. The cruciferous vegetables are great for the liver.

*Please keep in mind that the above is not a medical advice. You should see your doctor about any possible medical conditions.