Well... I found a - rather heavy - way to achieve this.
Briefly, I intersected the original bed files containing the scores with the multiintersected file to retrieve the score on the same intervals (bedtools intersect). I also retrieved the empty intervals (bedtools intersect -v). Then I concatenated, sorted and merged (bedtools merge -d -1 -scores collapse) those files to retrieve my multiintersected file with the original scores.
The output looks like this :
head ChIP_CiB-eg_R1+R2_multiinter_scores.bed
KhC1 0 139 0,0,0
KhC1 139 236 0,0,99.42199
KhC1 236 596 22.56072,0,99.42199
KhC1 596 725 22.56072,0,0
Nevertheless, the -score option would be useful for bedtools multiinter !

Mathieu