In this article, I describe an alternative approach for fitting linear models with multiple high-order fixed effects. The strategy relies on transforming the data before fitting the model. While the approach is computationally intensive, the hardware requirements for the fitting are minimal, allowing for estimation in models with multiple high-order fixed effects for large datasets. I illustrate implementing this approach using the U.S. Census Bureau Current Population Survey data with four fixed effects. I also present a new Stata command, regxfe, for implementing this strategy.