  We show that a large class of satellite operators are rank-expanding; that
is, they map some rank-one subgroup of the concordance group onto an infinite
linearly independent set. Our work constitutes the first systematic study of
this property in the literature and partially affirms a conjecture of the
second author and Pinz\'on-Caicedo. More generally, we establish a
Floer-theoretic condition for a family of companion knots to have infinite-rank
image under satellites from this class. The methods we use are amenable to
patterns which act trivially in topological concordance and are capable of
handling a surprisingly wide variety of companions. For instance, we give an
infinite linearly independent family of Whitehead doubles whose companion knots
all have negative $\tau$-invariant. Our also results recover and extend several
theorems in this area established using instanton Floer homology.
