For one thing, I know that Jesuits are often ordained bi-ritually. I presume this is because of their long history of involvement in the East.
Jim,
Actually, no one is ordained bi-ritually. One is ordained according to a specific Rite and, in the case of those ordained in other than the Latin Rite, one is ordained to the service of a specific Church
sui iuris. A priest of any Church may, subsequently be accorded bi-ritual faculties (more precisely, but it seems as though it will never become common use - 'bi-ecclesial faculties') to either serve in or assist in another Church
sui iuris.
Priests of the Society of Jesus who are specifically ordained for the service of an Eastern or Oriental Catholic Church (one example being the former Superior General of the Society, ordained to the service of the Armenian Church
sui iuris) are ordained according to the Rite of that particular Church, but are subsequently accorded bi-ritual faculties in the Latin Rite - a requirement.
Jesuits who were initially ordained as Latins and subsequently accepted to the Society's 'Eastern Province' are, at that subsequent time, accorded the faculties of the Church which they will serve.
Many years,
Neil
PS Jim, will get you off moderated post status w/in the next couple of days. You seem to have slipped thru the cracks on that count.