potissimum

Potissimum is the adverb of potissimus, a superlative built on the old adjective potis, "able" - a family whose positive degree has dropped out of ordinary use, leaving the comparative potior and the superlative standing on their own.

What it adds over praecipue and maxime is preference between named alternatives, so it is at its most natural in questions: quid potissimum, what above all, out of everything on offer. Potius, "rather", is the comparative of the same set and behaves the same way. Possum shares the root, though the connection is no longer felt.