Question

What would happen if OH-ions were added to a very basic solution?

Answer 1

It would make the solution more basic, but probably not much so.

Explanation:

Say you have a solution of pH=12, that means there are `10^-2` moles of `OH^-` already present. To raise this to pH=13, you'd have to add `9.9xx10^-2` moles of `OH^-`, almost 10 times as much as already present.
Doubling the number of `OH^-`-ions would only raise the pH by 0.3 points.