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This question about Attacks of Opportunity with ranged weapons wasn't quite what I'm looking for.
Aside from the feats Combat Patrol, Snap Shot, and Improved Snap Shot, what ways can I improve my attack of opportunity range?
We have access to all non-3rd-party material, and are Mythic Tier 1.
Use a reach weapon. Users of reach weapons have an increased threatened range to the distance of the weapon.
As the thread you linked mentions;
You threaten all squares into which you can make a melee attack
So arguably, all you need is some way to make your arms longer or to use a melee weapon with the Improved Quick Draw feat.
Your threatened area matters for attacks of opportunity only inasmuch as you are hoping to get attacks from movement-based or action-based provokes:
Provoking an Attack of Opportunity: Two kinds of actions can provoke attacks of opportunity: moving out of a threatened square and performing certain actions within a threatened square.
Moving: Moving out of a threatened square usually provokes attacks of opportunity from threatening opponents. There are two common methods of avoiding such an attack—the 5-foot step and the withdraw Action.
Performing a Distracting Act: Some actions, when performed in a threatened square, provoke attacks of opportunity as you divert your attention from the battle.
These are not, however, the only kinds of opportunities for you take attacks of opportunity in. For example, the Greater Reposition feat states:
Whenever you reposition a foe, his movement provokes attacks of opportunity from all of your allies
This isn't based off of threatened squares or anything; it's not that the movement can provoke attacks: it just does provoke, at which point you just need the ability to make attacks of opportunity with ranged weapons and the ability to attack the opponent with it (the target being in range, not behind total cover, etc).
Similarly, the Greater Trip feat causes opponents to provoke attacks of opportunity from everyone when tripped (not just your allies).
Other feats, spells, and class abilities exist to accomplish this task. Basically, you want the Snap Shot feat and an ally who causes enemies to provoke. Alternatively, you can use the Peacebond and Greater Peacebond spell from a safe distance in the hopes that the targeted creatures choose to try and draw or re-draw their weapons. There are, as far as I'm aware, no great ways to force enemies to provoke non-threatened-squares-based attacks of opportunity from a safe distance without help.
Note, however, that even with Combat Reflexes you can only get maybe ten attacks of opportunity and that may eventually not be enough. However, since your GM has already granted you a Mythic tier, the Mythic Combat Reflexes feat can solve that problem for you.
Note also that features provoking attacks of opportunity not via threatened squares is controversial.
