  In 2003, Rodriguez-Villegas conjectured four supercongruences on the
truncated ${}_3F_2$ hypergeometric series for certain modular K3 surfaces,
which were gradually proved by several authors. Motivated by some
supercongruences on combinatorial numbers such as Ap\'ery numbers and Domb
numbers, we establish some new supercongruences on the truncated ${}_3F_2$
hypergeometric series, which extend the four Rodriguez-Villegas
supercongruences.
