As a character levels up in Pathfinder 2e, at every odd numbered level, they can increase their level of training in one skill. From Untrained to Trained, or, starting at level 3, from Trained to Expert, at level 7 from Expert to Master, and starting at level 15, from Master to Legendary proficiency.
For many of characters, what this means is that they will increase two skills to Expert at 3 and 5, increase those same two skills from Expert to Master and 7 and 9, and can then increase a third skill to Expert and then Master at 11 and 13, and then at 15, 17, and 19, increase those three Mastered skills to Legendary.
The Skill Training feat allows a player to add additional skills at the baseline level of Trained (as does allocating an ability boost to Intelligence), and Rogues gain a skill increase at every level (effectively doubling the number of Expert/Master/Legendary skills). But there are no other General Feat based options for increasing a skill beyond the level of Trained. That means unless you're playing a Rogue, you'll never have more than three skills (and no more than two below 13th level) at the maximum bonus attainable at a given level.
Unless.... Are there other ways to increase the proficiency rank of skills?