One workaround is to increase the size of the plate dimensions.
Analytical equations of thin square plates show that the natural frequency is proportional to 1/a^2 where a is the edge length of the plate. If you double the edge length, the natural frequency would go down by a factor of 4. Furthermore, if you change from Fixed Supports on the edges to Simply Supported (not sure how to do that with a solid mesh in Explicit) then the natural frequency would go down by another factor of 4. Lower natural frequencies of the plate may reduce the multiple impacts issue.