Some classes of linear conjugation problems for a four-dimensional vector that are solvable in closed form

We consider the structure of the set of piecewise meromorphic solutions for a homogeneous linear conjugation problem for a four-dimensional vector. We show that in the presence of three piecewise meromorphic solutions to the linear conjugation problem it is possible to construct a canonical system of solutions to the linear conjugation problem and distinguish some classes of problems that are solvable in closed form.