My question

Is there a way of connecting two such circuits (or any 2nd order passive resonant circuits) such that the resulting transfer function (4th order) is the product of those of individual 2nd order resonant circuits both having the same frequency (but not necessarily the same quality factors)?

Another way of phrasing this question is to ask if one can built a 4th order passive resonant circuit whose transfer function can be decomposed into a product of two 2nd order transfer functions having the same resonant frequency.

The transfer function would look something like this:

G(s) = G1(s)*G2(s) = [N(s)/(s^2 + a1*s + b)]*[M(s)/(s^2 + a2*s + b)]

where s is the Laplace parameter and N(s) and M(s) can be any polynomials of s with order not greater than 2.

Thanks