We consider a generalized-ensemble algorithm for coarse-grained simulations of biomolecules which allows the thermodynamic behavior of two or more sequences to be determined in a single multisequence run. By carrying out a random walk in sequence space, the method also enhances conformational sampling. Escape from local energy minima is accelerated by visiting sequences for which the minima are more shallow or absent. We test the method on an intermediate-resolution coarse-grained model for protein folding with 3 amino acid types and explore the potential for a large-scale coverage of sequence space by applying the method to sets of more than 1000 sequences. The resulting thermodynamic data are used to analyze the structures and stability properties of sequences covering the space between folds with different secondary structures.