I'm wondering the derivation of following partition functions corresponding to various ensembles:

$$ \begin{aligned} \Xi(V, T, \mu) & =\sum_N Q(N, V, T) e^{\beta \mu N} \\ \Delta(p, T, N) & =\sum_V Q(N, V, T) e^{-\beta pV} \\ \phi(V, E, \beta \mu) & =\sum_N \Omega(N, V, E) e^{\beta \mu N} \\ \Psi\left(V, T, \mu_1, N_2\right) & =\sum_{N_1} Q\left(N_1, N_2, T, V\right) e^{\beta \mu N_1} \\ W(p, \gamma, T, N) & =\sum_V \sum_{\mathscr{A}} Q(N, V, \mathscr{A}, T) e^{-\beta pV} e^{\beta \gamma \mathscr{A}} \end{aligned} $$ where $\mathscr{A}$ is surface area, and $\gamma$ is the surface tension.

I've followed the usual statistical mechanics textbook and find the way to derive the probability distribution of states (and therefore partition function) in canonical ensemble and grand canonical ensemble by applying the method of Lagrange multipliers. But for the other ensembles as mentioned above, it's not quite clear for me how to apply such techniques to derive the partition functions.

At the same time, it looks like all the formula have similar shape defined as a Laplace transform, so I somewhat guess that there should be a more systematic way to derive the partition functions that can be used for various statistical ensembles. Is there such thing?