  We present a detailed analysis of multiple production of the lightest CP-even
Higgs boson (h) of the Minimal Supersymmetric Standard Model (MSSM) at
high-energy e^+ e^- colliders. We consider the production of the heavier
CP-even Higgs boson (H) via Higgs-strahlung e^+e^- \to ZH, in association with
the CP-odd Higgs boson (A) in e^+e^- \to AH, or via the fusion mechanism e^+e^-
\to \nu_e \bar\nu_e H, with H subsequently decaying through H \to hh, thereby
resulting in a pair of lighter Higgs bosons (h) in the final state. These
processes can enable one to measure the trilinear Higgs couplings \lambda_{Hhh}
and \lambda_{hhh}, which can be used to theoretically reconstruct the Higgs
potential. We delineate the regions of the MSSM parameter space in which these
trilinear Higgs couplings could be measured at a future e^+ e^- collider. In
our calculations, we include in detail the radiative corrections to the Higgs
sector of the MSSM, especially the mixing in the squark sector.
