The phase behaviour of long hard rods is independent of their length to breadth ratio in the limit that this ratio is very large. We form a binary mixture of rods with different length to breadth ratios but the same second virial coefficient. As the second virial coefficient is the same for both components, their phase behaviour in the pure state is identical. However, the difference in their shapes-one is longer and thinner than the other-results in an increased interaction between a pair of rods of different components. As the difference in shape of the two components is increased, first isotropic-isotropic coexistence is observed (with a critical point), then in addition nematic-nematic coexistence. At first there is a nematic-nematic critical point but this point reaches the isotropic-nematic transition, creating a four phase region. Gibbs’ phase rule, as usually stated, permits a maximum of three phases to coexist simultaneously in a binary athermal mixture. Here, the symmetry between the two components allows four to coexist.