Some diseases are due to germline mutations in predisposing genes, such as cancer family syndromes. Precise estimation of the age-specific cumulative risk (penetrance) for mutation carriers is essential for defining prevention strategies. The genotype-restricted likelihood (GRL) method is aimed at estimating penetrance from multiple case families with such a mutation. In this paper, we proposed an extension of the GRL to account for multiple trait disease and to allow for a parent-of-origin effect. Using simulations of pedigrees, we studied the properties of this method and the effect of departures from underlying hypotheses, misspecification of disease incidence in the general population or misspecification of the index case, and penetrance heterogeneity. In contrast with the previous version of the GRL, accounting for multiple trait disease allowed unbiased estimation of penetrance. We also showed that accounting for a parent-of-origin effect allowed a powerful test for detecting this effect. We found that the GRL method was robust to misspecification of disease incidence in the population, but that misspecification of the index case induced a bias in some situations for which we proposed efficient corrections. When ignoring heterogeneity, the penetrance estimate was biased toward that of the highest risk individuals. A homogeneity test performed by stratifying the families according to the number of affected members was shown to have low power and seems useless for detecting such heterogeneity. These extensions are essential to better estimate the risk of diseases and to provide valid recommendations for the management of patients.