The Leonine Prayers at the foot of the Altar after Mass represent a distictively nineteenth century way of dealing with a perceived need to seek urgent divine interventions in particular necessities. And, of course, there was always the possibility of saying a Votive or of adding additional Votive 'commemorations' to the proper prayers of the Day. (Not to mention the possibilities offered by the Litany form ... how very flexible our Western Liturgy has been.)
But there was once a practice which brought such ad hoc impetrations into the very heart of the Liturgy itself. Surviving texts look rather like responses to the occupation of Terra Sancta by Islamic forces. And, in terms of liturgical logic, they may not be a million miles away from the motive ascribed by Canon Arthur Couratin to the inclusion of Intercessions in the Byzantine Anaphora at the point they now occupy there; i.e., we secure the Presence of Almighty God upon the Altar so that we can then make use of It to tell Him what we want.
Thus, at Sarum. on certain days, the community was prostrate after the Santus; then, after the Libera nos and before the Pax ...; Psalms 78, 66, and 20 were recited 'in prostratione'; followed by Kyrie ... and Pater ..., versicles and responses; and three collects expressing this intention: ut Terram quam Unigenitus Filius tuus proprio sanguine consecravit, de manibus inimicorum crucis Christi eripiens, restituas cultui Christiano ...
A second part of this will describe the ancient Carmelite devotions.
In the splendid Altar-ready Sarum Missal produced this year by a learned and devout priest, you will find this provision on pages 330-331. I also gratefully thank Gregory diPippo for setting me on this track.
Psalms are numbered according to the Vulgate.