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I wonder, if there could be a Pareto Mixture Model, just like the Gaussian Mixture Model (GMM). How am I supposed to build a Pareto Mixture Model (PMM)?

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There can be mixture model using any distributions. Recall that mixture probability mass function, or probability density is

$$ f(x) = \pi_1 f_1 (x) + \pi_2 f_2 (x) + \dots + \pi_k f_k (x) $$

where $f_i$ are individual distributions and $\pi_i$ are weights such that $0 \le \pi_i \le 1$ and $\sum_i \pi_i = 1$.

I doubt there is software that will out-of-the-box implement such model for you, but you can easily estimate it's parameters using expectation-maximalization algorithm (in fact Wikipedia uses finite mixture model as example while describing it). Here you can find working EM code that can be adapted to mixture of Pareto distribution.

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