We prepare multi-component transition monocarbides of chosen composition by arc-melting together a pre-alloy of the transition metals and cast iron. Based on the elements Ti, Ta, V, Nb and W, 51 different binary, ternary and quaternary compositions are produced. The intrinsic hardness H and modulus E of the resulting iron-embedded carbide particles are directly measured using nanoindentation. Of all compositions tested here WC shows the highest modulus while two (Ta,V)C and (Ti,W)C carbides are shown to have a hardness 15% higher than that of all binary carbides; some (Ti,Ta,V)C compositions furthermore display interesting combinations of properties. The modulus and hardness variations with composition show that the valence electron concentration, which has been proposed to be a dominant parameter in predicting carbide hardness and modulus, is not a useful single predictor of optimal compositions. Other important parameters therefore also govern the hardness and modulus of MC carbides.