N=4 l-conformal Galilei superalgebras inspired by D(2,1;a) supermultiplets

N=4 supersymmetric extensions of the l-conformal Galilei algebra are constructed by properly extending the Lie superalgebra associated with the most general N=4 superconformal group in one dimension D(2,1;a). If the acceleration generators in the superalgebra form analogues of the irreducible (1,4,3)-, (2,4,2)-, (3,4,1)-, and (4,4,0)-supermultiplets of D(2,1;a), the parameter a turns out to be constrained by the Jacobi identities. In contrast, if the tower of the acceleration generators resembles a component decomposition of a generic real superfield, which is a reducible representation of D(2,1;a), a remains arbitrary. An N=4 l-conformal Galilei superalgebra recently proposed in [Phys. Lett. B 771 (2017) 401] is shown to be a particular instance of a more general construction in this work.