Consider a finite graph $G=(V,E)$. Suppose that I have two (not necessarily the same) percolation probabilities $\mathbb{P}_{1,p_1},\mathbb{P}_{2,p_2}$ on $\{0,1\}^E$ (e.g., $q$-Potts model) with parameters $p_1,p_2$, and define $\mathbb{P} = \mathbb{P}_{1,p_1}\cup \mathbb{P}_{2,p_2} $ to be the "union of two configurations", i.e., $$ \mathbb{P}_{1,p_1}\cup \mathbb{P}_{2,p_2}[\omega]=[\mathbb{P}_{1,p_1}\otimes \mathbb{P}_{2,p_2}][(\omega_1,\omega_2):\omega_1\cup \omega_2 =\omega] $$
Let's say these probabilities have well-defined ergodic limits once we take the appropriate infinite-graph limit (e.g., Potts model on larger and larger square lattices of $\mathbb{Z}^d$). Then can we determine the critical percolation probability $p_c$ of $\mathbb{P}$ if we know that of $\mathbb{P_1},\mathbb{P_2}$?
Indeed, it's clear that if either $p_1 > p_{1c}$ or $p_2 >p_{2c}$ are above the critical threshold for percolation of model $\mathbb{P_1},\mathbb{P_2}$, then $\mathbb{P}$ percolates. However, is it possible for $\mathbb{P}$ to percolate when $p_1<p_{1c},p_2<p_{2c}$? One could imagine an event when we have alternating chains configuration belong to $\omega_1,\omega_2$ such that each individual configuration does not percolation, but over all percolates.
For example, consider bond percolation in 1-dimensions. We can have an event where $\omega_1$ consists of all even bonds, and $\omega_2$ consists of all odd bonds. Then even though individually, they do not percolate, their union percolates.