Are there magical objects that increase the number of prepared spell for a wizard?

[Myth27]

Or objects with a similar effect that increases the flexibility of the spellcasting for wizards?

[ImproperJustice]

Pearls of power, ring of spell storing, and the Wizard’s hat.

Staves, scrolls, and wands all allow additional spell casting.

Ritual spells and unlimited cantrips give Wizards morr staying power in this edition than they have ever had.

[hymer]

Tome of Clear Intellect does it by increasing your Int. In a similar vein, the Headband of Intellect may help if your Int isn't very high.
Other than that, there are a lot of staffs and wands that allow you to cast spells from them. They can let you prepare other spells. And there is Ring of Spell Storing, and various spell scrolls.

Edit: Partially shadowmonk'ed.

[Kadesh]

They have the second best Ritual Casting in the game (it only needs to be in their book, and do not need to have it prepared - only a Tome Warlock can do it better, as they have access to every Ritual spell in the game provided they can find the scrolls).

If you're not yet Int 18+, increasing your Int helps - Headband of Intellect works wonders if you're multiclass and Int 16 or lower, while an Ioun Stone of Intellect (keep an eye out for Marbled Scarlet and Blue Spheres) helps you if you're 18, but don't have the ASI's for 20, but have a spare Attunement slot. The Tome of Clear Thought is something that you can use to increase it later on.

Also, there are literally dozens of magic items who provide "free" spell slots either by replicating spells effects (Ring of Featherfalling), or outright letting you cast the spells (staffs, scrolls), to the obvious one which allows you trade an unspent spell slot on one day to cast the spell another day.

[Sigreid]

Out of the Abyss has gems that can store spells.

[Tetrasodium]

artificer is int based, but not out yet. Eldritch knight & arcane trickster also give you their own prepped spells eventually. if you take a lot of ritual spells, those don't require you have them prepped as long as they are in your spellbook & wizards have a lotof those (although almost all low level spells).

[Myth27]

Tank you al for your answers.

[FirstBornSon]

There is nothing better than rod of absorption.

[Kadesh]

There is nothing better than rod of absorption.

o.O thst does nothing for the number of Spells Prepared, though.

[Laserlight]

Or objects with a similar effect that increases the flexibility of the spellcasting for wizards?

AOE spells and patience. I often open with Fireball, then stand back and let the meatshields clean up. The only time I even got close to running out of slots was:

Thief: "The giants aren't running out to investigate, they're turtling in the great hall."
Me: "So much for that plan. Let's sneak back out and try another way."
Barbarian: (yanks open door to great hall) "Hey ugly! Yer mother offered group discounts! Come at me, bro!"