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Once a spellcaster has reached 17th level and can cast 9th level spells, what more power can they try to obtain?
Before Mystra’s ban, there were 10th and higher level spells. Back in D&D3.5 there was Epic Magic. Now in 5th Edition, in lore, what spells or magic can the greatest wizards, sorcerers, or others seek to obtain?
Although it cannot be cast by players in this version, I suppose Epic Magic could still be a thing. As for elves, Elven High Magic would be a goal.
There are no higher-level spells in 5e than 9th level for player characters (that I know of)1. More powerful magic is more of a worldbuilding and storytelling tool. Yes Mythals and Elven High Magic still exist in the world, but not as something that player characters have access to.
For NPCs, getting access to and control over such high magic sources is a common story motive. For example, in Dungeon of the Mad Mage, Halaster and several other high level spellcasters are vying for control over the mythical source of power in the dungeon.
For PCs, once characters reach 20th level, the DM can award epic boons instead of higher level spells. These will improve the characters' spellcasting ability in some way beyond that of "normal" casters.
An epic boon is a special power available only to 20th level characters. (...) Epic boons can also be used as a form of advancement, a way to provide greater power to characters who have no more levels to gain.
These are certainly something to "strive for" as a player character. While they do not grant higher level spells, they enhance how well characters are able to use their existing spells. For what you are asking, the Boon of High Magic seems to be thematically the best fit:
BOON OF HIGH MAGIC You gain one 9th-level spell slot, provided that you already have one.
Other Boons that are concerned with better spellcasting are the boon of spell mastery, boon of spell recall, or boon of quick casting (all on p. 232 DMG).
It might be a nice capstone for the end of a campaign if the DM grants the players control over one of the high magic resources in the world, and they then become NPCs shaping the world in further adventures for new groups of PCs. (We did that with many of our high level characters at the end of campaigns across various editions of D&D, it is a pretty satisfying experience for closing things out).
1 As Joel points out in his answer, you technically can cast a 9th level spell as if it were 10th level with the help of the Book of Exalted Deeds. While I think that's not what your asking for, it is a pretty cool exception.
Artifacts
Artifacts typically provide game-breaking abilities, even for level 20 characters. Even your example of level 10 spells can be achieved in some circumstances. The Book of Exalted Deeds has this:
Enlightened Magic. Once you've read and studied the book, any spell slot you expend to cast a cleric or paladin spell counts as a spell slot of one level higher.
Other artifacts typically offer particular spells which can be cast a number of times per day.
Magic Items
Level 20 characters are expected to have a couple of these even in lower magic campaigns, but the more the merrier.
Wands and staves are clearly thematic in terms of spells cast per day. However, don't overlook the various Tomes, which can increase your casting stat up to 30, and thus improve your casting effectiveness.
Epic Boons
Epic boons are provided at DM discretion, but come with a variety of possible spellcasting benefits. You could gain things like an additional 9th level slot, the ability to cast a level 1 spell at will, or the ability to cast a spell without consuming a slot (even 9th level).
Epic Boons also have lesser cousins, Blessings. The examples given include increasing your casting stat (and thus all your spellcasting).
Feats
These can be trained as rewards, according to the DMG and at DM's discretion, and several provide additional magical abilities. Magic Initiate and Ritual Caster from the PHB give some flexibility. Tasha's offers several, including Artificer Initiate, Eldritch Adept, Fey Touched, Metamagic Adept, Shadow Touched, Telekinetic, and Telepathic.
Written spells
Wizards specifically don't have a cap on spells in their spellbooks, and may always be interested in tracking down additional spells to copy. Some Warlocks and those with the Ritual Caster feat may be interested in tracking down written rituals.
Multiclassing
There are several classes that could provide additional flexibility for casters, at the expense of the core class's capstone ability and a possible feat or stat points. While a three level dip can only net you level 2 spells, they can be upcast with your higher level spell slots. Any such class will noticeably increase your number of cantrips.
The Pact of the Tome Warlock will net you even more cantrips, plus the possibility of access to the Book of Ancient Secrets and the potential to learn any ritual regardless of class.
The Arcana Domain Cleric (Sword Coast Adventurer's Guide) gains some extra Wizard cantrips on top of the usual Cleric ones.
Friends
Spellcasting need not necessarily be your own. High level characters may ally with powerful archfiends, angels, fey, and deities.
