A recent generalization of the Jahn-Teller coordinate proposed for modeling cusps on single-sheeted adiabatic potential energy surfaces for triatomics is extended to any type of crossing seam. The model is applied to the (2)A" state of NO2 and the more complicated HN2((2)A') system, which shows permutationally equivalent and strongly curved seams. (C) 2016 Published by Elsevier B.V.