I am engaged to marry a woman who lives in Switzerland. We both have sizable incomes and we do not want to pay substantially more taxes in either country. Currently I file single. When I simply changed the status of my filing in TurboTax from single to Married filing separately, the tax burden increased. Why did this happen? Am I doing something wrong?

tax burden increased if you included your spouse's income. If your income was the same prior to and subsequent to changing status, an error occured with software.

Agree to an extent. The "marriage penalty" was revoked several years ago.

However, filing MFS does invoke some prohibitions on your return that may affect the tax you owe. I do not have enough information to determine if any of the prohibitions apply to you.