These two moods will be treated together because they have the same meaning and are practically interchangeable in use. They differ in form as well as stylistically.
Form: Subjunctive I is a synthetical form which survived from Old English. It has only one form, which is homonymous with the verb stem: be, do, have, go, write, etc.
The Suppositional Mood is an analytical form which is built up with the help of the auxiliary verb should for all persons + the Infinitive. The non-perfect Suppositional mood: should be, should do, should write. The perfect Suppositional Mood: should have been, should have done, should have written.
Meaning: Both Subjunctive I and the Suppositional Mood express problematic actions, not necessarily contradicting reality. These actions are presented as necessity, order, suggestion, supposition, desire, request, etc.
Expressing the same kind of modality, Subjunctive I and the Suppositional Mood are used in the same syntactic structures and are, to a great extent, interchangeable. However, they differ stylistically: thus, in the British variant of the English language Subjunctive I is only preserved in elevated prose, poetry or official documents. In neutral, everyday speech the Suppositional Mood is used. In American English Subjunctive I in neutral and colloquial speech is the norm:
He even suggested that I should play cricket with his sons (Br.E.).
He suggested that I come for her (Am.E.).
Use: A. Simple Sentence
In simple sentences only Subjunctive I is used in a few set expressions as a survival of old usage (the so-called formulaic expressions).
1. Most of them express a wish:
Long live the Army!
Success attend you!
Be yours a happy meeting!
Far be it from me to spoil the fun / to conceal the truth.
Suffice it to say that he is a liar.
God bless you! God save the Queen! Heaven forbid!
Confound your ideas!
Subjunctive I in such expressions can be replaced by “may + Infinitive”:
May success attend you! May your meeting be happy!
May the Army live long!
2. Some formulaic expressions have a concessive meaning:
Happen (come) what may (will).
Cost what it may.
So be it (Be it so).
Subjunctive I in these expressions may be replaced by Let + Infinitive:
Let it be so.
3. The only productive pattern of a simple sentence with Subjunctive I is the sentence expressing a command or a request with an indefinite pronoun as the subject:
Everybody leave the room!
Somebody switch off the light!
Subjunctive I may be replaced in such sentences by “let + Infinitive”:
Let everybody leave the room.
4. The Suppositional Mood is used only in one type of interrogative sentences beginning with And what if …? (А что если вдруг …?):
And what if he should come back?