Summary: The article by S. Monni and M. G. Tadesse [ibid. 4, No. 3, 413–436 (2009; Zbl 1330.62035)] introduces a model for relating large numbers of predictors and responses. That situation typically occurs when investigators are in an exploratory mode. This discussion argues that in such situations the fairly strong assumptions of Monni and Tadesse (e.g., linear regression models with common coefficients for all variables within a cluster of responses) may be counterproductive. If such models are to be used, it is critical that model fit be assessed before relying on their results.