Is every first order phase transition related to a second order phase transition by the tuning of some coupling? In practice is the expectation that the this tuning can usually be done in the lab. (By playing with the temperature, density, magnetic and electric fields and/or particle numbers.)
I suppose the answer is no. Consider a transition between the solid-state phase and the gas or liquid phase. Gas and liquid phases are translationally invariant. In a solid crystal, translational invariance is broken due to the presence of lattice. According to the acepted point of view, a continuous transition between phases with different symmetries is impossible. This in particular is a reason for the absence of critical points in solid-liquid phase transitions.
There is an Ising model I've modified that displays both first and second-order phase transitions, and I do employ tuning to magnetize the cellular automaton.
Tuning in this example is the frustration of the system between its Moore and von Neumann neighborhods. When the neighborhoods are tuned from 4 and 5 cells up to 6, the system enters a ferromagnetic transition.