Archives of Nethys (https://2e.aonprd.com/) is the official online source for Pathfinder information. They have a search function you may get some use out of.
Only one ability seems to remove the immunity to Demoralize
Braggart Swashbucklers (Advanced Player's Guide) can at level 9
When such a Swashbuckler performs a Finisher attack, they gain this benefit from Exemplary Finisher
If the foe was temporarily immune to your Demoralize, their temporary immunity ends.
This affect is unavailable to Swashbuckler Multiclass, so you would have to select Swashbuckler as your actual class.
There are other sources of Frightened, if that's what you're after
Feat (Intimidation Skill) - Scare to Death
Attempt an Intimidation check against the Will DC...
Critical Success The target must succeed at a Fortitude save against your Intimidation DC or die. If the target succeeds at its save, it becomes frightened 2 and is fleeing for 1 round; it suffers no effect on a critical success.
Success The target becomes frightened 2.
Failure The target becomes frightened 1.
Feat, Stance (Monk, Martial Artist Archetype) - Dragon Roar
Prerequisites Dragon Stance Requirements You are in Dragon Stance. Effect You bellow, instilling fear in your enemies. Enemies within a 15-foot emanation must succeed at a Will save against your Intimidation DC or be frightened 1 (frightened 2 on a critical failure). [...] Creatures in the area of your roar are then temporarily immune for 1 minute.
Marshal Archetype - Dread Marshal Stance
Critical Success Your marshal's aura increases to a 20-foot emanation, and it grants you and allies a status bonus to damage rolls equal to the number of weapon damage dice of the unarmed attack or weapon you are wielding that has the most weapon damage dice. When you or an ally in the aura critically hits an enemy with a Strike, that enemy is frightened 1.
Success As critical success, but your aura's size doesn't increase.
Spell (Wizard Focus, Feat for Enchantment School) - Dread Aura*
Cast [Two Actions] somatic, verbal; Area 30-foot-radius emanation centered on you; Duration sustained up to 1 minute. You emit an aura of terror. Foes in the area are frightened 1 and unable to reduce the condition.
Spell (Bard Focus, Feat) - Dirge of Doom*
Cast [Single Action] verbal; Area 30-foot emanation; Duration 1 round. Foes within the area are frightened 1. They can't reduce their frightened value below 1 while they remain in the area.
Spell (Witch (APG) Cantrip for Curse Patron Theme) - Evil Eye
Cast [Single Action] somatic; Range 30 feet; Targets 1 creature; Saving Throw Will; Duration sustained up to 1 minute. [...]The target becomes frightened based on the results of its Will save. This condition value can't be reduced below 1 while the spell is active and you can see the target. Regardless of the outcome, the target is then temporarily immune for 1 minute.
Failure The target is frightened 1.
Critical Failure The target is frightened 2.
Item - Dread Blindfold
The first time a particular creature sees you in a day, it must succeed at a DC 37 Will save or be frightened 1. This is an emotion, fear, and mental effect, and your allies become immune to it after about a week.
Item - Gorget of the Primal Roar (this is an Intimidation check, not a Demoralize attempt)
Activate [Single Action] command; Frequency once during the duration of each polymorph effect; Requirements You’re in a non-humanoid form via a polymorph effect; Effect You unleash a bestial roar, attempting a single Intimidation check compared to the Will DCs of all enemies within 30 feet to impose the effects below. Though this activation has the command component, you can issue this command without the need for language.
Critical Success The creature is frightened 2.
Success The creature is frightened 1.
Consumable - Dread Ampoule (alchemical bomb)
On a hit, the target becomes frightened 1, or frightened 2 on a critical hit.
*These Focus Spells can be acquired with the classes' Multiclass Archetypes but may require a very high level.
Antagonize doesn't let you re-use Demoralize, but it may make the Frightened Condition last longer.
When you successfully Demoralize a creature, its frightened condition can't decrease to less than 1 at the end of its turn until it either uses a hostile action against you or can no longer observe or sense you for at least 1 round.
Remorseless Lash will also extend your ability to keep Frightened on targets, if you have access to Hobgoblin (Uncommon) Feats.
When you succeed at a melee weapon Strike against a frightened foe, that foe can’t reduce their frightened condition below 1 until the beginning of your next turn.