Can a binary star host three giant circumbinary planets?

We investigate the orbital stability of a tilted circumbinary planetary system with three giant planets. The planets are spaced by a constant number (Δ) of mutual Hill radii in the range Δ = 3.4–12.0 such that the period ratio of the inner pair is the same as that of the outer pair. A tilted circumbinary planetary system can be unstable even if the same system around a coplanar binary is stable. For an equal-mass binary, we find that the stability of a three-planet system is qualitatively similar to that of a two-planet system, but the three-planet system is more unstable in mean motion resonance regions. For an unequal-mass binary, there is significantly more instability in the three-planet system as the inner planets can undergo von Zeipel–Kozai–Lidov oscillations. Generally in unstable systems, the inner planets are more likely to be ejected than the outer planets. The most likely unstable outcome for closely spaced systems, with Δ ≲ 8, is a single remaining stable planet. For more widely separated systems, Δ ≳ 8, the most likely unstable outcome is two stable planets, only one being ejected. An observed circumbinary planet with significant eccentricity may suggest that it was formed from an unstable system. Consequently, a binary can host three tilted giant planets if the binary stars are close to equal mass and provided that the planets are well spaced and not close to a mean motion resonance.