Use the +level, or -level-color options to adjust the white/black points. This will generally give the mask the effects of "dodging" or "burning"; which, compose Screen
will respect.
convert source.jpg \
\( mask.jpg -normalize +level 0,60% \) \
-compose screen -composite destination.jpg
You can also adjust the opacity of the mask by defining an alpha channel with -alpha, -channel & -evaluate. See this question. But this wouldn't work with compose Screen
as it's expecting a range between black & white.
convert source.jpg \
\( mask.jpg -alpha set -channel A -evaluate set 60% \) \
-compose screen -composite \
destination.jpg