Grass-legume mixtures characterized by high productivity, efficient nitrogen (N) use and strong weed suppression were proposed to increase sustainability of grassland production. Adding competitive forbs to grass-clover mixtures can be expected to further enhance the high productivity of grass-clover mixtures. This study investigates whether and to what extent adding forbs to a grass-clover mixture results in yield gains, and estimates the contributions of forb species (identity effect) and interactions with the grass-clover mixture (diversity effect) to these gains. It further examines the effectiveness of weed suppression in forb-containing grass-clover mixtures. Fifteen pure and mixed stands, all comprising the grass Lolium perenne L. and the legume Trifolium pratense L., and one or three competitive forb species (Cichorium intybus L., Carum carvi L., Plantago lanceolata L.) were established in a two-year field experiment and fertilised at two levels of N application. The diversity effect between P. lanceolata and the L. perenne-T. pratense mixture and a strong identity effect of P. lanceolata jointly contributed to yield gains of 10–21% over the binary L. perenne-T. pratense reference mixture for a wide range of P. lanceolata proportions across years and N fertilisation levels. In contrast, comparably smaller diversity and/or identity effects of C. intybus and C. carvi resulted in maximal yield gains of 5% and 7%, respectively, occurring at a narrower proportional range, but also in yield losses at high forb proportion. Including up to 80% forb in the L. perenne-T. pratense mixture effectively maintained weed suppression, but the degree of weed suppression decreased with increasing forb proportion in the following year. Including selected forbs, especially P. lanceolata, in productive grass-clover mixtures is promising for further enhancing productivity, meanwhile effectively suppressing short-term weed growth in intensively managed grasslands.