We recently introduced a new approach to the evaluation of weight of evidence (WoE) for Y-chromosome profiles. Rather than attempting to calculate match probabilities, which is particularly problematic for modern Y-profiles with high mutation rates, we proposed using simulation to describe the distribution of the number of males in the population with a matching Y-profile, both the unconditional distribution and conditional on a database frequency of the profile. Here we further validate the new approach by showing that our results are robust to assumptions about the allelic ladder and the founder haplotypes, and we extend the approach in two important directions. Firstly, forensic databases are not the only source of background data relevant to the evaluation of Y-profile evidence: in many cases the Y-profiles of one or more relatives of the accused are also available. To date it has been unclear how to use this additional information, but in our simulation-based approach its effect is readily incorporated. We describe this approach and illustrate how the WoE that a man was the source of an observed Y-profile changes when the Y-profiles of some of his male-line relatives are also available. Secondly, we extend our new approach to mixtures of Y-profiles from two or more males. Surprisingly, our simulation-based approach reveals that observing a 2-male mixture that includes an alleged contributor's profile is almost as strong evidence as observing a matching single-contributor evidence sample, and even 3-male and 4-male mixtures are only slightly weaker.