Here's a generic solution for finding three peaks that overlap from N input files, with more than 20% overlap between peak pairs.

$ bedops -u file1.bed file2.bed ... fileN.bed \
    | bedmap --echo --echo-map --fraction-both 0.2 - \
    | awk -F"|" '(split($2, a, ";") == 3)' \
    > answer.bed

If peaks within one input file overlap by more than 20%, it is possible they will be in answer.bed if there is a third qualifying pair. But you can parse this file to filter those out, so that what is left are pairings between peaks from three different inputs. One easy way is to preprocess the inputs, appending an ID tag that ties an element to its input file, then use that ID after mapping to filter any within-ID pairs.