Simulate $n$-PDA with $n-1$-PDA
Yes, any PDA with $n&gt;2$ stacks can be simulated by a pda with $2$ stacks. It is possible to show this without explicitly using Turing machines.

Assume that you have $n$ stacks, with contents $\alpha_1$ to $\alpha_n$. Store all these stacks on top of each other, with special separator symbols $\square_i$. So a single stack contains $\square_1\alpha_1 \dots \square_n\alpha_n$ (top left). Now assume that I want to perform an operation on stack $k$ (look at the top, check it is empty, push or pop symbols). In order to do this use the second stack. Move all stacks up to the $k$th to the second stack (popping from the one pushing to the other). The two stacks are now $\square_1\alpha_1 \dots \square_k\alpha_k$ and $\alpha^R_n\square_n\dots \alpha^R_{k+1}\square_{k+1}$. it is now easy to operate on stack $k$ (since it is on top of one of the stacks). and in general we continue moving the $n$ stacks around between the two stacks to  continue the simulation.