It can be called ♦ subjunctive III.

Of major importance for the category of mood description is the question of time expression in the oblique mood. As for the actual expression of time, they render time relatively, by means of the aspective category of retrospective coordination: the non-perfect forms of the verbs in the subjunctive (past indefinite for subjunctive II and future-indefinite-in-the-past for subjunctive III) express the relative present - the simultaneity or posteriority of unreal actions, while the perfect forms (past perfect for subjunctive II and future-perfect-in-the-past for subjunctive III) are used to express relative past - the priority of unreal actions, stressing their actual failure. Cf.: I am sure that if she tried she would manage it (the simultaneity or posteriority in the present). – I was sure that if she tried she would manage it (the simultaneity or posteriority in the past). – I am sure that if she had tried she would have managed it (the priority and failure of the action in the present). – I was sure that if she had tried she would have managed it (the priority and failure of the action in the past).

One more type of the oblique mood is subjunctive IV(traditionally referred to as “modal suppositional”). It is built with the help of modal verbs, and expresses the same semantic types of unreality as subjunctive I: may/might + infinitive – is used to denote wish, desire, hope, and supposition in some contexts (with the words “whatever, however, though”): May it be so! (subjunctive I: Be it so!); I hoped he might come soon (cf.: I hoped that he come soon); should + infinitive – is used to express supposition, suggestion, speculation, recommendation, inducements of various types and degrees of intensity: Whatever my mother should say about him, we’ll marry one day (subjunctive I: Whatever my mother say about him, we’ll marry one day). One more type of modal constructions is constructions with the semi-notional verb “to let” expressing inducement(побуждение): Let’s agree to differ; Let him do it his own way! These constructions are semantically identical with constructions of subjunctive I but used in grammatically different environments: subjunctive I inducements are used only with the second person, while let + infinitive inducements are used in all other cases, cf.: Do it your own way. – Let me do it my own way. - Let us do it our own way. – Let him do it his own way, etc.

Subjunctive IV can express relative present, simultaneity or posteriority, through its imperfect forms (the present imperfect), or it can render the relative past, the failure of some imaginary action in priority through its perfect forms (the present perfect). см прим ю16

The system of the oblique moods can be presented in the following table:

Subjunctive I (spective) Form: bare infinitive (imperfect) Meaning: attitudes Example: Be it so!	Subjunctive II (stipulative conditional) Form: the past (imperfect or perfect) Meaning: unreal condition Example: If she tried…
Subjunctive IV (modal spective) Form: modal verbs + bare infinitive (imperfect or perfect) Meaning: attitudes Example: May it be so!	Subjunctive III (consective conditional) Form: future-in-the-past (imperfect or perfect) Meaning: consequence of unreal condition Example: … she would manage it.