The Solemn Intercessions on Good Friday, both OF and EF, pray for the following:
1. For Holy Church;
2. For the Pope;
3. For all orders and degrees of the faithful;
4. [EF 5.] For catechumens;
5. [EF 7.] For the unity of Christians [Previously, For Heretics and Schismatics];
6. [EF 8.] For the Jewish people [For the Conversion of the Jews];
7. [EF 9.] For those who do not believe in Christ [Previously, For the Conversion of Pagans];
8. For those who do not believe in God*;
9. [EF 4.] For those in public office [Previously, For the Roman Emperor†];
10. [EF 6.] For those in tribulation [For the necessities of the faithful].
* The growth of atheism has necessitated the addition of a prayer for atheists.
† There having been no Holy Roman Emperor since 1806, it was understandable that this prayer – long omitted (though I have seen it prayed for Queen Victoria, in a 19th C. Holy Week book, and I assume it was still used in Austria-Hungary until its collapse) – was replaced by a prayer for all those in civil office.
But who is not prayed for? The faithful departed, those who have died.
Furthermore, while even in the last pre-Conciliar order of service, the Libera nos still asked for the intercession of the Saints, that phrase was deleted in the Novus Ordo.
A petition could well be added, therefore, in private, somewhat after this fashion, using the Collect for the Living and the Dead, plus a modified form of the matching Secret, turned into an introductory petition, thus:
Oremus et pro vivis et defunctis: ut Deus, cui soli cognitus est numerus electorum in superna felicitate locandus, intercedentibus omnibus Sanctis suis, universorum, quos in oratione commendatos suscepimus, et omnium fidelium nomina, in beatæ prædestinationis libro adscripta retineat.Oremus.Flectamus genua.Levate.Omnipotens sempiterne Deus, qui vivorum dominaris simul et mortuorum, omniumque misereris, quos tuos fide et opere futuros esse prænoscis: te supplices exoramus; ut, pro quibus effundere preces decrevimus, quosque vel præsens sæculum adhuc in carne retinet, vel futurum jam exutos corpore suscepit, intercedentibus omnibus Sanctis tuis, pietatis tuæ clementia omnium delictorum suorum veniam consequantur. Per Dominum nostrum, Jesum Christum, Filium tuum, qui tecum vivat et regnat in unitate Spiritu Sancti, Deus, per omnia sæcula sæculorum. R. Amen.
(Let us pray for the living and the dead: that God, to whom alone is known the number of the elect to be placed in supernal happiness, through the intercession of all his Saints, may retain written in the book of blessed predestination the names of all who have been recommended to our prayers, and of all the faithful.(Let us pray.(Let us kneel down.(Arise.(Almighty and eternal God, who hast dominion over both the living and the dead, and hast mercy on all, whom thou foreknowest shall be thine by faith and good works: we humbly beseech thee, that those, for whom we have resolved to make supplication, whether the present world still holds them in the flesh, or the world to come has already received them out of the body, may, through the intercession of all thy Saints, obtain of the goodness of thy clemency pardon for all their sins. Through our Lord Jesus Christ, thy Son, who with thee liveth and reigneth in the unity of the Holy Ghost, God, world without end. R. Amen.)
This is lengthier than the other intercessions, but does sum up them all, and prays, beseeching the prayers of the Saints, for all the dead, as well as all the living. Thus it seems to me we should pray on Good Friday, when Christ died to save all.