The powers known column in the class table is usually the start and end of the discussion about how many powers you know. You cannot usually add more other than through explicit options (Expanded Knowledge, etc.). Manifesters generally behave similarly to sorcerers in this respect
Erudite psions, yes
Complete Psionic has a variant psion known as the erudite. It’s at the end of the book, there’s at least one major ambiguity in its description, and it’s potentially very powerful, but it does exist and with a little sanity-checking it can be in line with other psionic options.
Erudites maintain a psionic repertoire, which is similar to a wizard’s spellbook. The erudite adds to his repertoire through psionic interaction with other manifesters, in a lengthy process in which the two meditate and psionically connect. Or, alternatively, they can add powers from a power stone to their repertoire.
Then erudites have a unique stat called Unique Powers per Day. This number indicates how many different powers the erudite may manifest in a day; this limits them in how many powers they effectively “know” in a given day. This is also where the major ambiguity of the class comes in: its own description contradicts itself, sometimes implying that the limit is a total, across all power levels, and at other times implying that the number is per power level, where you get that many unique powers per day for each power level. And it never outright explicitly states either. Since erudites get as high as 9th-level powers, this ambiguity means your interpretation changes the total number of unique powers by a factor of 9, which is immense.
With UPD as a total, rather than per level, the erudite is quite reasonable, actually probably a little weaker than the regular psion. The UPD number only ever gets as high as 11, after all; that’s not very many. But if you read it as per level, that’s 99 different powers and that’s absurd. The UPD-per-level erudite is by-far the most powerful manifester in the game, a Tier 1 class. Other Tier 1 classes keep up with it, though, since the e.g. Sor/Wiz spell list is better than the Psion power list.
The other thing to be aware of is “Spell-to-Power” erudites. This is an option presented in a Mind’s Eye article for erudites, and allows erudites to learn spells as if they were powers, adding them to their repertoire. On the face of things, this is a good idea since a lot of settings don’t have a lot of manifesters for erudites to interact with, plus magic always got a lot more support than psionics, but it’s also a massive power boost. For the UPD-total erudite, it’s still pretty manageable, but the StP UPD-per-level erudite is basically the most powerful class in the game. It effectively can learn every power and spell in the game, and can use 99 different ones each day. Obviously, you probably don’t want to allow that.