New exotic examples of Ricci limit spaces

For any integers $m\geqslant n\geqslant 3$, we construct a Ricci limit space $X_{m,n}$ such that for a fixed point, some tangent cones are $\mathbb{R}^m$ and some are $\mathbb{R}^n$. This is an improvement of Menguy's example. Moreover, we show that for any finite collection of closed Riemannian manifolds $(M_i^{n_i},g_i)$ with $\mathrm{Ric}_{g_i}\geqslant(n_i-1)\geqslant 1$, there exists a collapsed Ricci limit space $(X,d,x)$ such that each Riemannian cone $C(M_i,g_i)$ is a tangent cone of $X$ at $x$.