It is well-known that the Dirac equation is a "Relativistic wave equation" which describes all spin-1/2 massive particles such as electrons and quarks. The Dirac equation, as a system of linear differential equations, is derived from the relativistic energy-momentum quadratic relation. Definitely, there is the same derivation approach for the Weyl equation describing spin-1/2 massless particles, as it is just a special case of the Dirac equation.
On the other hand, in physics, the energy–momentum relation is the relativistic equation relating a particle's ("with any spin") rest mass, total energy, and momentum.
Now one may ask could other Relativistic wave equations, which describe other massive (and massless) particles with various spins, also be derived from the energy-momentum relation (by a derivation procedure similar to the Dirac equation)? If the answer in no, then one may ask why not?, Why only the Dirac equation is derived from such approach? Sorry if the question doesn't make sense somehow.