Two-dimensional Hotelling models predict that firms choose to maximally differentiate on one characteristic and minimally differentiate on the other characteristic. Strong evidence shows that a max-min equilibrium is attained. This study uses the 2010-2017 data from the Texas Comptroller of Public Accounts to examine the joint choices of geographic location and product positioning (or brand) by multi-unit operators. We argue that, assuming that the geographic location is the dominant characteristic and the product positioning is the dominated characteristic, the model implies that multi-unit owners structure their establishment portfolios to be geographically differentiated while choosing less differentiated brands. Alternatively, if the geographic location is the dominated characteristic and the product positioning is the dominant characteristic, the model implies that multi-unit owners locate their establishments near one another in a geographic space while choosing highly differentiated brands. The empirical findings indicate a max-min (min-max) equilibrium, which provides insights into the strategic motivations of multi-unit owners and, within their decisions, the relevant dominance of place versus market position.