  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.
