Look ahead mate selection (LAMS) schemes have been proposed to improve longer-term genetic merit when both selection and crossbreeding are important. We investigate the performance of a LAMS scheme which includes both predicted progeny merit and predicted grandprogeny merit in a mate selection index (MSI). Simulation of a multibreed beef population, with additive breeding values, direct and maternal breed effects and direct and maternal heterosis was used to compare response from the LAMS scheme to mate selection on progeny merit only (PROG), selection on estimated breeding value (EBV) followed by random mating (RAND) and a structured crossbreeding scheme (CROSS). An additional strategy, LAMS + CO, was similar to LAMS but included a negative weighting on the coancestry of selected animals in the MSI to reduce inbreeding. LAMS gave up to 3% greater response in generation eight than PROG, 4·5% greater response than RAND, and 15% greater response than CROSS. Results from LAMS + CO were very similar to LAMS but inbreeding was 11% less from LAMS + CO at generation eight. The advantage of LAMS and LAMS + CO over PROG in later generations was hypothesized to be the result of positive assortative mating and greater use of maternal effects. Evidence to support the hypothesis of assortative mating was a positive significant correlation of EBVs of mates (sires and dams) in LAMS and LAMS + CO but not in PROG. Strategies PROG, LAMS and LAMS + CO all created closed populations of animals with optimum composite breed proportions.