School of Occultism.

Wizardry urges the relentless pursuit of knowledge that pushes every boundary in search of greater power and understanding, but some boundaries are never meant to be crossed. Occultisms care not for these limitations, peering behind cosmic veils, devouring forbidden secrets, and pushing their understanding of spellcraft until reality itself tears open. It is from the strange, alien realms that are revealed which they draw even greater power, shattering all limits no matter the eldritch consequences.

Level 2 Features:

Forbidden Knowledge.

In your study of proscribed power, you learn Deep Speech or another language of your choice.
In addition, choose a 1st-level spell from the warlock spell list. You add it to your spellbook if it's not there already, and it is a wizard spell for you.

Intrusion.

Your search into the forbidden reaches beyond the universe yields great power but comes at the risk of letting something from beyond intrude into your reality.
You have an Intrusion Die, which starts at a d6, that can change as you use your features. The die can increase or decrease, along this progression of die sizes: d2, d3, d4, d6, d8, d10, d12.
The size maximum for your Intrusion Die is its starting size, which increases by one step when you reach certain levels in this class: 5th level (d8), 11th level (d10), and 17th level (d12).
When you use a feature that risks Intrusion, roll your Intrusion Die. On a 2 or higher, no Intrusion occurs, and the Intrusion die reduces in size one step on the progression.
On a roll of 1, the Intrusion Die rises in size one step, and you roll on the Intrusion table to determine what happens as reality fractures. Intrusions use your spell save DC.
The Intrusion Die increases in size by one step (up to its starting size) when you finish a short rest, and it resets to its starting size when you finish a long rest. Additionally, you can focus alien potency into your spells. When you cast a spell using a spell slot, you can risk Intrusion to choose one of the following.
Overwhelming Mind. One target of the spell has disadvantage on the first saving throw made against it.
Seeking Eye. You have advantage on the first attack roll you make for the spell.

Level 6 Feature:

Reality Tear.

Choose a spell of 3rd level or lower from the warlock spell list. You add the spell to your spellbook if it's not there already, and it is a wizard spell for you. When you cast the spell, you can risk Intrusion to remove the need to Concentrate on it, and the spell ends after 1 minute or its normal duration, whichever is shorter. Additionally, you can cause an automatic Intrusion (and increase the die's size one step, up to its starting size) to cast the spell once without a spell slot, and you regain the ability to do so when you finish a long rest.

Level 10 Feature:

Focused Conjuration.

When you cause an Intrusion, you can roll twice on the Intrusion table and choose which result to use, and you can negate the Intrusion by gaining 1 level of exhaustion. Additionally, you gain one of the benefits below, and you can change your chosen benefit when you finish a long rest. As a bonus action, you can cause an automatic Intrusion (and increase the die's size one step, up to its starting size) to change your chosen benefit.
Alien Consciousness. You gain immunity to the charmed and frightened conditions, and you can't be possessed.
Cosmic Resistance. You gain resistance to necrotic and psychic damage.
Spatial Domination. You gain a flying speed equal to your walking speed and can hover.

Level 14 Feature:

Durable Summons.

The nature of distance and location is revealed for the lie that it is. You add the Scrying spell to your spellbook, if it's not there already.
When you cast Scrying, you can risk Intrusion to choose one of the following.
All Knowing. Treat your connection to a target creature as if you have part of its body.
All Seeing. Change the spell's casting time to 1 action. When you cast Scrying, during the spell's duration, you can cause an automatic Intrusion (and increase the die's size one step, up to its starting size) to teleport yourself, and any willing creatures within 10 feet of you, to unoccupied spaces you can see through the scrying sensor. Once you teleport in this way, you can't do so again until you finish a long rest.