In the case of Toulman Boatwright Jr v. Grace Boatwright, five justices recused themselves. Apparently the COA needs six for a quorum so the Miss. S. Ct appointed Hon. Hollis McGehee to sit as a sixth COA Justice on the case. See the Order here. The Boatwrights divorced in 2004 and have been litigating various matters arising out of the divorce ever since.
This can’t happen very often, I would think.