Is It Possible To Filter Only Bookend Reads From A Bed File?

I have a bed file with many fragments, some overlapping, some on their own and some adjacent to each other (book-ended) features.

I know can group overlapping and book-ended features using bedtools like

bedtools cluster -i fragments.bed

However I was wondering if anyone knew of a way of obtaining from the input file only the fragments that contain book-ended adjacent fragments.

Any ideas?

Best regards