One limitation of a Psion is that they get only so many powers known and you basically can't exceed that amount. But there is another rule, Independent Research - one week and 200 xp per power level - and you create completely new power, or duplicate the one that already exists. The question is, can you use it to learn more powers than you usually are able to?
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The independent research guidelines are intended to be worked out between a DM and a player to allow the player to do interesting or unique things with their character. This can, in some cases, be used to power up (or power down) a character if necessary.
But the Psion is a pretty powerful class. The limitation on the number of powers known is fairly tight, but it’s not nearly as tight as, say, Psychic Warrior or Wilder (who have real problems in this area). Psions can do very well on their allotted number. On the other hand, especially if you want some flavorful powers, maybe the DM agrees they shouldn’t “count” towards your limit, seeing as that limit is pretty tight.
Ultimately, though, the rules themselves do not automatically allow the Psion to exceed their limit, or to even use those rules. They only give suggestions to DMs for what the costs of that sort of thing should be when they want to allow it.
This is not entirely clear from the rules text.
Personally, I would recommend against making independent research be in addition to what the class table suggests as a number of powers known, for the following reasons: