This paper studies a linear model for multidimensional panel data of three or more dimensions with unobserved interactive fixed-effects. The main estimator uses double debias methods, and requires two preliminary steps. First, the model is embedded within a two-dimensional panel framework where factor model methods in Bai (2009) lead to consistent, but slowly converging, estimates. The second step develops a weighted-within transformation that is robust to multidimensional interactive fixed-effects and achieves the parametric rate of consistency. This is combined with a double debias procedure for asymptotically normal estimates. The methods are implemented to estimate the demand elasticity for beer.