We present a study of \bar pp collisions with a leading antiproton and a rapidity gap in addition to that associated with the antiproton. The second gap is either within the region available to the proton dissociation products, \bar p+p\rightarrow (\bar p+{gap})+X+{gap}+Y, or adjacent to the outgoing proton \bar p+p\rightarrow (\bar p+{gap})+X+({gap}+p). Results are reported for two-gap to one-gap event ratios and compared with one-gap to no-gap ratios and with theoretical expectations.

PACS numbers: 13.85.Ni, 11.55.Jy, 12.40.Nn