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Flat bands are of extreme interest in a broad spectrum of fields since givenby their high degeneracy, a small perturbation introduced in the system is ableto push the ground state in the direction of an ordered phase of interest.Hence the flat band engineering in real materials attracts huge attention.However, manufacturing a flat band represents a difficult task because itsappearance in a real system is connected to rigid mathematical conditionsrelating a part of Hamiltonian parameters. Consequently, whenever a flat bandis desired to be manufactured, these Hamiltonian parameters must be tunedexactly to the values fixed by these rigid mathematical conditions. Here wedemonstrate that taking the many-body spin-orbit interaction (SOI) into account-- which can be continuously tuned e.g. by external electric fields --, theserigid mathematical conditions can be substantially relaxed. On this line weshow that a $\sim 20-30 \%$ variation in the Hamiltonian parameters rigidlyfixed by the flat band conditions can also lead to flat bands in the same or ina bit displaced position on the energy axis. This percentage can even increaseto $\sim 80 \%$ in the presence of an external magnetic field. The study ismade in the case of conducting polymers. These systems are relevant not onlybecause they have broad application possibilities, but also because they can beused to present the mathematical background of the flat band conditions in fullgenerality, in a concise, clear and understandable manner applicable everywherein itinerant systems.

Spin-orbit interactions may relax the rigid conditions leading to flat bands