Parallel caps transfer function
The math doesn't work that way. In general, be careful not to assume equations can just be extended by throwing in more variables in a form that looks similar, especially when it is just tossing things into more than one place )in this case, both numerator and denominator). Fractions just don't work that way. It doesn't make any intuitive mathematical sense if you actually think about it.

\$ Z = \frac{Z_1Z_2}{Z_1+Z_2} \$ is a shortcut formula for only two resistances.

The real base formula from which it is derived is:

\$\frac{1}{Z} = \frac{1}{Z_1} + \frac{1}{Z_2} +...+\frac{1}{Z_n}\$

I don't even remember or use the simplified two-Z equation. I only ever use the base form.