The great Catholic Anglican theologian, Dr Eric Mascall, writing at the time when Concelebration was the new sexy -ation among trendy Western liturgists, put in a spirited defence of the practice of the Private Mass. If, he said, you want to make the point to somebody that the Eucharistic Sacrifice is One Sacrifice ... not a lot of similar sacrifices but the same sacrifice ... the best thing you can do is to take him him into a church with a lot of altars and a priest standing muttering silently at each, and tell him that each of those men is doing the same action. Mascall was probably thinking of the Church of S Mary Magdalene in Oxford, then a great Catholic centre but now sadly most terribly lapsed. It was there that, except when he was on the rota to celebrate in Christchurch Cathedral, he said his daily Mass, old style, Introibo ad Altare Dei through to Et Verbum caro factum est. Not infrequently, every altar was occupied by a priest offering that same eternal sacrifice. One thinks also of the Shrine Church at Walsingham, its twenty or so altars abuzz with sacrifice. Come to think of it, that's probably why the lower basilica at Lourdes has an altar to each of the fifteen mysteries of the Holy Rosary. One can imagine palmy days when priests were queuing up on rotas to say their masses and making, each of them, the customary arrangement with the priest just before him or the one just after, to serve his Mass in return for him serving yours.
And despite the contempt into which the Private Mass fell in the decades after Vatican II, I am convinced that it should be put back into the repertoire of every-day Western Catholicism. Not when there are laypeople needing a Mass: it is obviously the duty of a priest to serve that need (and a desire to say an additional Mass solo would not be a sufficient reason for binating). Nor do I feel that a Private Mass is appropriate when it is not possible to find a layperson to answer it and there is a public Mass which one would be welcomed to concelebrate. But we should remember that Vatican II did preserve inviolate the right of every priest to celebrate a Private Mass, with one or two caveats (e.g.; not during a concelebration within the same church). And subsequent magisterial documents have repeated this right. And successive editions of the Novus Ordo Missal have provided (and, most recently, revised) the rite for celebrating the 'New Mass' privately.
But ... cat-out-of-the-bag ... I do feel that the opportunity to say a private Mass is also the opportunity to return to roots, resourcissement, by saying the ancient Western Rite. The unlatined could use the English Missal which, for decades, was the rite of Catholic Anglicans. It's what those adverts in the Church Times of fifty years ago meant when a church invited you to attend it by flaunting the lovely phrases 'Western Rite' and 'Full Catholic Privileges'.