There are manifolds (rationally elliptic) $M_1$ and $M_2$ of different rational homotopy types but their rational cohomology algebras coincide. Such examples were discussed in Nishimoto, Shiga, Yamaguchi's joint work ("Elliptic rational space whose cohomologies and homotopies are isomorphic"). In this paper, they defined a family of minimal algebras and proved that their cohomology algebras are the same but rational homotopy types are different.

However, the minimal algebras they have considered have generators of the same degree. i.e. both the minimal algebras have the same generating sets but the differentials are different.

Is it possible to have two minimal algebras (rationally elliptic) having different degree generators but their cohomology algebras agree?