Configuration-constrained calculations of potential-energy surfaces in even-even superheavy nuclei reveal systematically the existence at low excitation energies of multiquasiparticle states with deformed axially symmetric shapes and large angular momenta. These results indicate the prevalence of long-lived, multiquasiparticle isomers. In a quantal system, the ground state is usually more stable than the excited states. In contrast, in superheavy nuclei the multiquasiparticle excitations decrease the probability for both fission and alpha decay, implying enhanced stability. Hence, the systematic occurrence of multiquasiparticle isomers may become crucial for future production and study of even heavier nuclei. The energies of multiquasiparticle states and their alpha decays are calculated and compared to available data.