In this question, it is proven that any manifold $M$ which is also a Co-H space is in fact a simply-connected homology sphere. That is, $M$ is a manifold, is simply connected, and has the homology of a sphere.
There are examples of such spaces which are not simply spheres, for example the Poincaré homology sphere.
If I only ask that $M$ is a $\mathbb{Z}$-Poincaré duality space (that is a space which exhibits Poincaré duality in its homology/cohomology with coefficients in $\mathbb{Z}$) is a similar result known?
Looking at the proof in the aforementioned question, it seems to use the classification of manifolds, so would not apply in this situation.
Alternatively, are there examples of spaces which are Co-H, and Poincaré duality spaces, but are not homology spheres?