  Twisting a given knot $K$ about an unknotted circle $c$ a full $n \in
\mathbb{N}$ times, we obtain a "twist family" of knots $\{ K_n \}$. Work of
Kouno-Motegi-Shibuya implies that for a non-trivial twist family the crossing
numbers $\{c(K_n)\}$ of the knots in a twist family grows unboundedly. However
potentially this growth is rather slow and may never become monotonic.
Nevertheless, based upon the apparent diagrams of a twist family of knots, one
expects the growth should eventually be linear. Indeed we conjecture that if
$\eta$ is the geometric wrapping number of $K$ about $c$, then the crossing
number of $K_n$ grows like $n \eta(\eta-1)$ as $n \to \infty$. To formulate
this, we introduce the "stable crossing number" of a twist family of knots and
establish the conjecture for (i) coherent twist families where the geometric
wrapping and algebraic winding of $K$ about $c$ agree and (ii) twist families
with wrapping number $2$ subject to an additional condition. Using the lower
bound on a knot's crossing number in terms of its genus via Yamada's braiding
algorithm, we bound the stable crossing number from below using the growth of
the genera of knots in a twist family. (This also prompts a discussion of the
"stable braid index".) As an application, we prove that highly twisted
satellite knots in a twist family where the companion is twisted as well
satisfy the Satellite Crossing Number Conjecture.
