In this paper we extend the Multiple Indicator Solution (MIS) so that it can also be used to account for endogeneity when there are interactions between observed and unobserved factors in the specification of the utility function. We develop the theoretical derivation and illustrate it with a revealed preference case study of mode choice. Policy indicators such as time elasticity and value of time are discussed. The results are compared with a logit model and with an Integrated Choice and Latent Variable (ICLV) model. Results show that endogeneity is present in the case study and that the proposed variation of the MIS method is practical and able to account for it. Our proposed method can be seen as a starting point for the practical detection and treatment of this type of endogeneity without the drawbacks of multifold integration. (C) 2016 Elsevier Ltd. All rights reserved.