Does having a high salary change how many allowances you should claim?
If the only variable that is changing in your equation is salary, it should not affect the number of allowances you claim on your w-4. The IRS publishes tables that help employers figure out how much tax to withhold, and it automatically scales up with income.
There are many other factors that affect how many allowances you should claim such as whether you have a spouse who is working, lots of tax deductions, etc. But those are outside the scope of this question.
High income alone doesn't impact the number of allowances you claim. But there are some complexities which is why the W-4 has several worksheets.
Two-Earners/Multiple Jobs Worksheet. If you have two jobs or both spouses work you need to make sure you use this part of the form otherwise each job will withhold taxes based only on the income they are paying you. That can lead to too little tax being withheld.
Deductions, Adjustments, and Additional Income Worksheet is used not just for people who will be itemizing. It is also used by those with more complex income taxes which could include income from rental property, or income for selling stocks or mutual funds. This worksheet is to adjust for people who don't get 99% of their income from thir employer, or will be itemizing.
As to how many should you claim?
That depends on your exact tax situation. The goal for many taxpayers is to make the numbers workout in the end so that they either owe a little or get a small refund. If they are too far from zero, then they will adjust the number of allowances up or down to make their goal the following year.
As others have noted, the short answer is: No.
Read the instructions on the form. It tells you how to calculate the number of allowances. If you're filling out the form, the instructions should be right there in front of you. Basically, you get allowances for yourself and any children, and possibly extra allowances based on filing status, i.e. married or head of household.
You can claim additional allowances if you plan to itemize deductions and your deductions will be at least $4,200 more than the standard deduction for your filing status. So your income could INDIRECTLY affect the number of allowances, as if you have a large income, you might have more deductions.