We analyze the effect of point mutations on the energy landscape of a coiled-coil peptide, GCN4-pLI, where the native state is a parallel tetrameric configuration formed from two identical dimers. Experimentally, a single mutation, E20S, supports both antiparallel and parallel structures. Here, we analyze the potential energy landscapes of the dimeric units for the parent sequence and four mutants, namely E20S, E20A, E20P, and E20G. Despite sharing characteristic funnels containing the parallel and antiparallel structures, the point mutations change some parts of the landscape quite dramatically, and we predict new intermediate structures and characterize the associated heat capacities. For the mutants we predict that kinked intermediate structures facilitate the transition between parallel and antiparallel morphologies, in contrast to the parent sequence. Furthermore, we predict a change from a multifunnel energy landscape in the E20S mutant to a landscape dominated by an underlying single funnel in the parent sequence, with accompanying heat capacity signatures. Our results imply that changes in the landscape due to mutations might provide useful tools for functional protein design.