I have a trust that outlines how my estate is handled when I die.

You can amend your trust, amendments are simply done, no special formalities are required. But you must clearly set forth the identity of the trust, what paragraphs are being amended, and clearly state the changes. Think of this as how an uninformed third party would view the amended trust, after your demise, and that may help you to draft an amendment, if you are doing so yourself.

Keep in mind that residuary gifts should match up with the tax allocation clause in your trust, and also consider non-probate transfers and how the statutory presumption works in your state for allocation of the tax burden. Otherwise, your beneficiaries may be surprised to find out that they are paying the taxes on other people's specific gifts and bequests, or on transfers made by bank account designations or retirement plan designations. Your state's law (or your trust's provisions) may lump taxes and other expenses of trust administration onto the residue, so that your residual gifts would pick-up those costs. This could exonerate the specific gift beneficiaries from paying part of the cost of such items.

The answer is that while it is easy to write the amendment you seek, there may be an inadvertent reallocation of taxes or expenses when you do so. I don't like to be the bearer of unpleasant news, but I have to tell you that you should invest in a review of what you want to do with an Arizona estate planner who can discuss the statutory presumption on allocation of tax burden and costs of administration with you and take a look at the instructions in your trust on that point. Also, keep in mind that if your non-probate beneficiaries are not the same people as your residuary trust beneficiaries, divergences of interest can pop up if your estate has a heft tax or administrative cost burden.