  In this work we show how the composition of maps allows us to multiply,
enlarge and move stable domains in phase and parameter spaces of discrete
nonlinear systems. Using H\'enon maps with distinct parameters we generate many
identical copies of isoperiodic stable structures (ISSs) in the parameter space
and attractors in phase space. The equivalence of the identical ISSs is checked
by the largest Lyapunov exponent analysis and the multiplied basins of
attraction become riddled. Our proliferation procedure should be applicable to
any two-dimensional nonlinear system.
