How can I use different price tiers for a customer?

Answer: You can't.

What you can do is to give a discount specifically for this client for one particular SKU (or any client and couple SKUs if desired). 

Discounts are covered in this article.

For example:
Let's say you want to set price tier 1 for a customer but for one particular item you give him a discount $2 because he found a better price. 
You can set a discount rule "$2 off" (or you can use %) and specify the discount for the product as per example:

Here I set a discount rule for all customers with the tag, but you can also specify individual discounts for customers.

Note: The price for this item is $10

However, when I click on the Apply discounts button the price changes to $8.

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