It is shown that any elliptic K3 surface with a section and with two $II^*$-fibres is sandwiched by a Kummer surface in a very precise way.
Shioda Tetsuji. "Kummer sandwich theorem of certain elliptic K3 surfaces." Proc. Japan Acad. Ser. A Math. Sci. 82 (8) 137 - 140, November 2006. https://doi.org/10.3792/pjaa.82.137