  We present an innovative cluster-based method employing linear combinations
of diverse cluster mean-field (cMF) states, and apply it to describe the ground
state of strongly-correlated spin systems. In cluster mean-field theory, the
ground state wavefunction is expressed as a factorized tensor product of
optimized cluster states. While our prior work concentrated on a single cMF
tiling, this study removes that constraint by combining different tilings of
cMF states. Selection criteria, including translational symmetry and spatial
proximity, guide this process. We present benchmark calculations for the one-
and two-dimensional $J_1-J_2$ and $XXZ$ Heisenberg models. Our findings
highlight two key aspects. First, the method offers a semi-quantitative
description of the $0.4 \lessapprox J_2/J_1 \lessapprox 0.6$ regime of the
$J_1-J_2$ model - a particularly challenging regime for existing methods.
Second, our results demonstrate the capability of our method to provide
qualitative descriptions for all the models and regimes considered,
establishing it as a valuable reference. However, the inclusion of additional
(weak) correlations is necessary for quantitative agreement, and we explore
methods to incorporate these extra correlations.
