  We present an exactly solvable model of equal spin $s_1$ dimer single
molecule magnets. The spins within each dimer interact via the Heisenberg and
the most general quadratic global and local (single-ion) anisotropic spin
interactions, and with the magnetic induction ${\bf B}$. For antiferromagnetic
couplings and $s_1>1/2$, the low temperature $T$ magnetization ${\bm M}({\bm
B})$ exhibits $2s_1$ steps of universal height and midpoint slope, the $s$th
step of which occurs at the non-universal level-crossing magnetic induction
$B_{s,s_1}^{\rm lc}(\theta,\phi)$, where $\theta,\phi$ define the direction of
${\bm B}$. The specific heat $C_V$ exhibits zeroes as $T\to0$ at these
$B_{s,s_1}^{\rm lc}(\theta,\phi)$ values, which are equally surrounded by
universal peak pairs as $T\to0$. The non-universal $B_{s,s_1}^{\rm
lc}(\theta,\phi)$ values lead to a rich variety of magnetization plateau
behavior, the structure and anisotropy of which depend upon the various global
and local anisotropic spin interaction energies. We solve the model exactly for
$s_1=1/2$, 1, and 5/2, and present ${\bm M}({\bm B})$ and $C_V({\bm B})$ curves
at low $T$ for these cases. For weakly anisotropic dimers, rather simple
analytic formulas for ${\bm M}({\bm B})$ and $C_V({\bm B})$ at arbitrary $s_1$
accurately fit the exact solutions at sufficiently low $T$ or large $B$. An
expression for $B_{s,s_1}^{\rm lc}(\theta,\phi)$ accurate to second order in
the four independent anisotropy energies is derived. Our results are discussed
with regard to existing experiments on $s_1=5/2$ Fe$_2$ dimers, suggesting
further experiments on single crystals of these and some $s_1=9/2$ Mn$_4$]$_2$
dimers are warranted.
