  Let $X$ be a K3 surface over a number field. We prove that $X$ has infinitely
many specializations where its Picard rank jumps, hence extending our previous
work with Shankar--Shankar--Tang to the case where $X$ might have potentially
bad reduction. We prove a similar result for generically ordinary
non-isotrivial families of K3 surfaces over curves over
$\overline{\mathbb{F}}_p$ which extends previous work of Maulik--Shankar--Tang.
As a consequence, we give a new proof of the ordinary Hecke orbit conjecture
for orthogonal and unitary Shimura varieties.
