Compressible fluid dynamical systems are traditionally derived from a kinetic theory by either a Hilbert or Chapman-Enskog expansion in small Knudsen number. These derivations fail to produce formally well-posed systems beyond the compressible NavierStokes system, which arises as a first order correction to the Euler system. Here we offer an alternative derivation that produces a family of compressible fluid dynamical systems. The first two systems are again the Euler and Navier-Stokes systems, but one can go further. Every system in the family dissipates entropy and is formally well-posed over domains without boundary. The validity of these systems formally extends into transition regimes. These systems extend the compressible Navier-Stokes system and also extend a class of fluid dynamical systems developed by Maxwell, Kogan, Sone, and others that are not derivable from the Navier-Stokes system.