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?
Best Answer
Other Classes
You've mentioned Rogue as getting additional skill increases and that they're able to use those to get 6 legendary skills by level 20, but Investigators also have that same ability to get a skill increase each level.
Specific Skills
Quite a few options exist to grant legendary proficiency in specific skills (often increasing proficiency to legendary at 15th level), including the following:
Treated as Higher Proficiency
Similarly, there are a few options that allow characters to act as though they have a higher skill rank for some particular purpose. I'll include Perception in these even though it technically isn't a skill:
Companions
If you're fine with a companion having the skill proficiency, then there are a few other options:
The Construct Innovation of the Inventor can gain legendary proficiency in Intimidation, Stealth, Survival, and any Intelligence- or Charisma-based skills of the character's choice through the Miracle Gears revolutionary modification and/or Marvelous Gears breakthrough modification.
Ranger animal companions can become legendary in Stealth at 16th level with Stealthy Companion and Specialized Companion as an Ambusher.
18th-level Specialized Companions of the Animal Trainer archetype gain legendary Performance, instead of another skill increase from the specialization.