When you have too many deductions--especially high property taxes--this can trigger AMT, eliminating some or all of your ability to deduct them. This is affecting an increasing percentage of taxpayers.
Step 1: Understand your marginal tax rate under AMT
The first thing you should do is understand your situation using tax software. Increase and decrease your salary by a few thousand dollars and watch the impact on your taxes due. You may be unpleasantly surprised to learn that you're in an effective 35% tax bracket.
Step 2: Maximize all available tax shelters
Maximize all available tax shelters that aren't exempt from AMT: 401k, HSA, refinancing mortgage with points, charity gifts, etc. If your employer provides a tax-sheltered profit sharing plan, find out if you can forego some salary in exchange for maximizing contributions.
Consider borrowing money to maximize tax shelters
If you can't afford to maximize your shelters in the short term before the end of the year, AMT results in a high enough effective bracket, it may pay to temporarily use high-interest rate loans or credit cards to fund the tax-shelters. I would do this only as long as you're confident you can pay them back in a few months, or else the interest fees could offset the tax savings. You can get a cash advance (with a fee) or plan in advance and don't pay the credit card's full balance so you can instead build up cash to contribute to tax shelters. You would only want to do this if you're sure you can pay the credit card or other loan back before the interest rate overtakes the tax savings.
Another way to manage AMT is if you are in the fortunate situation where one year you might be exposed to it and another year you may not. You want to shift as much income to the year(s) in which you are paying no AMT, so that you use up as much of the non-AMT income range as possible. You can also shift charitable contributions to the AMT year, where you'll get a deduction at the AMT marginal rate.
Consider shifting income
Take advantage of it your employer allows you to directly shift income between years. Alternately, shift your deductions that aren't subject to AMT to the years where you are expecting AMT. Examples: pay mortgage interest early, refinance with points, etc. You can also shift income around if you can't afford to maximize tax shelters each year by strategically maximizing them in the years you are hitting the AMT. Again, consider loans if you have to.
Strategically sell taxable securities
You can also increase or decrease taxable income by selling taxable securities at a loss or profit as appropriate between years.