I would like to make a higher gravity beer, an Amber specifically. With the yeast (Dry Yeast - Safale S-04) I currently use, I get stuck at about 5.8% ABV (SG 1.074, current gravity 1.030). Do I need yeast starter? Do I need to use a different type of yeast? Are some yeasts better in more alcoholic conditions?
White labs Super High Gravity (WLP099) yeast claims to be alcohol tolerant up to 25% ABV. Normally most ale yeast shouldn't have a problem with 1.074 sg. Perhaps a yeast starter or better temperature control is needed.
But for a stuck fermentation right now pitch some champagne yeast. It won't mess with the flavor and is great to get the gravity down. It is very commonly used for RIS and Barley wines.
5.8% ABV is not considered "higher gravity". There should be no problem S-04 or most any dry or liquid yeast up until closer to 10% ABV.
It sounds like your fermentation is either stuck or simply not complete.
When did you brew? What size packet of S-04? Did you pitch the whole packet? What fermentation temperature? Did you do anything for aeration/oxygenation of wort? What was your brewing procedure; did you do a full-volume boil, or top up with water?
Wort is what determines fermentability in general, not yeast. Almost any ale yeast can easily ferment a 10+% beer. But if you don't make a fermentable wort, the yeast doesn't matter. Many times extract beers are less fermentable due to the way the extract is made. An all grain beer mashed at a high temperature or with large amounts of less fermentable malts like crystal can finish high, also. If you have consistently high FGs, look first at your recipe and ingredients.