Can a creature train to gain feats?

Question

Can a creature spend gp on training to acquire more feats?

For example, a typical level 1 human has 2 feats. Is there any way he can pay for extra training to get another feat? What's the going rate for learning a new feat?

Answer 1

No, they cannot.

But there are certain types of feats that can be obtained that would increase your max feats, like story and achievements feats, which some GMs allow their players to take as bonus feats at first level to better suit a character into the campaign.

Magic and combat schools

The magic schools from Inner Sea Magic and combat schools from Inner Sea Combat can grant you (free) extra feats for those who are members of certain organizations, like Extra Ki to members of the Houses of Perfection, and members of a monastery dedicated to Cayden Cailean could gain Toughness as a bonus feat after going through the Gauntlet of Inebriation.

Keep in mind that those rules presented on both books are optional, and though some of them can be seen in adventure paths (official campaigns) or some pathfinder society scenarios, GM discretion is required to use them.

See also the faction journal cards, sometimes they offer bonus feats on specific seasons.

Mythic feats

Feats granted by mythic tiers are in addition to those gained by your character levels, as such, they are also additional bonus feats if mythic rules are being used on your table.

Answer 2

Yes, but not the way you are thinking. You can spend gp to purchase items that grant you feats, including slotless items, but training does not allow one access to feats in the same way that practice and experience with a thing have no impact on one's ability to do that thing. Specifically, you can gain:

• Any/all combat feats, Any/all grit feats, Any/all style feats (though those are also all combat feats so far, so...), Deadly Dealer, Dampen Presence, Psychic Sensitivity, and any/all feats listing Expert Sniper as a prerequisite (though that's currently only the Master Sniper feat, which is also a combat feat)
  • This is gained via the second method of Ioun Stone resonant power generation, via a result of 26, and is the set of all feats gainable via rogue talents (unlike normal selection, you can gain talents multiple times this way). Each power requires a stone set in a wayfinder, and while a wayfinder may have any number of slots for ioun stones, this rapidly becomes quite expensive. Pricing guidelines are absent regarding specific powers, or power combinations.
• Several other feats via other rolls on that same table, namely:
  • Alertness (19)
  • Quicken Spell (24)
  • Run (25)
  • Brew Potion (32)
  • Fleet (75)
• One other feat not otherwise available can be gained from regular Ioun Stone use, namely:
  • Endurance from the Scarlet and Green Cabochon
• several other items grant feats, but the feats granted are redundant to the above.
• If your GM lets you create an item of At-Will paragon surge, you can use said item to gain up to at least 50 feats, or all of them you can qualify for if you possess access to a Plane with Timeless magic. Post errata, you can only get any 1 you qualify for per day, but you can still get all of them with access to a Timeless plane. The estimation system estimates the price of such an item at 60,000 gp, but it should really cost more, since it gives your party all the feats.
• You can gain any one feat you qualify for by purchasing a scroll of Plane Shift keyed to a timeless plane, and a scroll of Paragon Surge for the feat you want. This costs 1,500 gp. If you want to come back from the plane afterwards, that costs 2,625 gp instead (for a second plane shift scroll. Unlike ioun stones, such permanent spells can be dispelled.