An intuitive generalization of the explicitly covariant single-body relativistic dynamical equation to multiple multiple interacting particles is difficult. The no-go theorem of Currie Jordan and Sudarshan is an example of the difficulties to device such explicitly covariant version of relativistic interacting particles. I do not know if a satisfactory elegant solution was found.
A book that explains this problem is
FROM CLASSICAL TO
Giampiero Esposito, Giuseppe Marmo
Form of relativistic dynamics with world lines