So the question is: when is it permitted to use “Eucharistic Prayer for Use in Mass for Various Needs IV”, which has the title “Jesus, Who Went About Doing Good”?
In the rubric after the title it has:
“1. the following form of this Eucharistic Prayer is appropriately used with Mass formularies such as, For Refugees and Exiles, In Time of Famine or For Those Suffering Hunger, For Our Oppressors, For Those Held in Captivity, For Those in Prison, For the Sick, For the Dying, For the Grace of a Happy Death, and In Any Need.”
These Masses come from the part of the Roman Missal with the title “Masses and Prayers for Various Needs and Occasions”.
The General Instruction of the Roman Missal discusses them in n. 368 to 378. I think the key sentence about when they may be done is:
“374. If any case of a graver need or of pastoral advantage should arise, at the direction of the Diocesan Bishop or with his permission, an appropriate Mass may be celebrated on any day except Solemnities, the Sundays of Advent, Lent, and Easter, days within the Octave of Easter, the Commemoration of All the Faithful Departed (All Souls’ Day), Ash Wednesday and the days of Holy Week.”
A rough estimate of how many days this is:
Solemnities 12
Sundays of Advent 4
Sundays of Lent 5
Octave of Easter 8
All Souls’ Day 1
Ash Wednesday 1
Days of Holy Week 7
total: 38 days
So with 365 days in a year this leaves about 327 days of the year that the Priest may use “Eucharistic Prayer for Use in Mass for Various Needs IV”.
The General Instruction of the Roman Missal also has: “369. In view of the rather broad possibilities of choice among the readings and orations, it is desirable that Masses for Various Needs and Occasions be used in moderation, that is, when truly required.”
[Excerpts from the English translation of The Roman Missal © 2010, International Commission on English in the Liturgy Corporation. All rights reserved.]