Perhaps at some point or another, Chase and co. could be bought back to when the Earth was created, and theres nothing but hot and steaming barren rock, and an unusual temple in the distance.
They could choose to enter this temple, or choose to leave. You probably have to, as you need pieces of a key to unlock the entrance. The key parts are scattered around the game.
If they enter, they enter one much like the one in AvP: a temple that shifts between forms. However, you do this by a flick of a switch.
During your exploration, you may encounter a rare enemy:

Whisper from the past
Possible Battle Memory description: A shard of memory long before even Giegue's race had learnt the secrets of PSI. Speaks of forgotten lore.
Appearance: A figure hidden in shadow, and it has something like runes surrounding it's body.
Attack moves:
-The dark figure's attack is inexplicable! (typeless PSI attack at a party member. Note that typeless means you don't have any immunity against it whatsoever!)
-The dark figure's attack is incomprehensible! (spot the difference? same as the first one, but stronger.)
-The dark figure used PK Teleport at something! It replicated! (summons another Whisper of the past)
Now, as soon as there are 5 Whispers of the past, they do something special. What happens here is in order:
-Every dark figure concentrated! (Nothing)
-Every dark figure released their runes into the air! A ritual is performed! (Fully heals all of them.)
-A spell is cast! You feel a sensation akin to getting torn apart! (PK Crash)
-The exausted figures faded into nothing more than mere memory. (They all flee the battle. Note that this move happens at the same turn that they cast PK Crash.)
Every one of them have a very, and i mean VERY small chance of dropping an item regardless of whether you manage to defeat them or not: Piece of ancient lore.

If you go through the temple with precise and exceptionally complicated moves, eventually you reach somewhere that looks like a library. You can read the scrolls if you wish.
They will concern a rather special PSI technique that unfortunately led to unfortunate results, and eventually forbidden. However, there is a tapestry nearby that is perfect for studying relics.
If you bring Piece of ancient lore here, you can study it. as soon as you studied 5 of those, you get the item: ??? (yes, thats it's name.) Then you are bought straight back to modern times.
Examining ??? will reveal specific instructions on how to create a special PSI stone. The ingredients are all hard to come by.
If you succeed in the task, you will get: Strange stone. If you use it on a PSI wielder in your party, this happens.
(party member) feels the power of the ones long ago run from the stone into your very body and mind! (party member) learnt PK Crash!
What is PK crash? well...

PK Crash:
Description: A PSI forbidden by ancient law. Tear the fabric of reality apart!
Does a ridiculously high amount of damage at an enemy, and there is a good chance of dealing an instant KO. However you are affected by it as well!
The collateral damage deals moderate damage to everyone in your party, and a chance of instant KO too! Though the chances are less.
Judging to the overpowered nature of this PSI power, all that hard work would be worth it, even if it takes, i dunno, 1 month to get it?