Gorman Engel curves are extended to incomplete systems. The roles of Slutsky symmetry and homogeneity/adding up are isolated in the rank and functional form restrictions for Gorman systems. Symmetry determines the rank condition. The maximum rank is three for incomplete and complete systems. Homogeneity/adding up determines the functional form restrictions in complete systems. There is no restriction on functional form in an incomplete system. Every full rank and minimal deficit reduced rank Gorman system has a representation as a polynomial in a single function of income. This generates a complete taxonomy of indirect preferences for Gorman systems. Using this taxonomy, we develop models of incomplete Gorman systems that nest rank and functional form and satisfy global regularity conditions. All results are completely derived with elementary and straightforward methods that should be of wide interest.