In the "pre-jammed" mode when the density of the configuration is low and when the particles are mobile, the compression and expansion can be stopped, if so desired. Then the LSA, in effect, would be simulating a granular flow. Various dynamics of the instantaneous collisions can be simulated such as: with or without a full restitution, with or without tangential friction. Differences in masses of the particles can be taken into account. It is also easy and sometimes proves useful to "fluidize" a jammed configuration, by decreasing the sizes of all or some of the particles. Another possible extension of the LSA is replacing the hard collision force potential (zero outside the particle, infinity at or inside) with a piece-wise constant force potential. The LSA thus modified would approximately simulate molecular dynamics with continuous short range particle-particle force interaction. External force fields, such as gravitation, can be also introduced, as long as the inter-collision motion of each particle can be represented by a simple one-step calculation.