  Previously one of the authors constructed uncountable families of groups of
type $FP$ and of $n$-dimensional Poincar\'e duality groups for each $n\geq 4$.
We strengthen these results by showing that these groups comprise uncountably
many quasi-isometry classes. We deduce that for each $n\geq 4$ there are
uncountably many quasi-isometry classes of acyclic $n$-manifolds admitting free
cocompact properly discontinuous discrete group actions.
