I never really answered your question. I'm not a teacher, just a native U.S. speaker. I have NEVER heard of a "suppositional mood." In English class in high school (and it was honors English and I did really well on the big standardized SAT English test) we learned a bit about the subjunctive and promptly forgot it. The "suppositional?" Never.

I am skeptical of the existence of any such "mood," it sounds like overanalysis. It has all the earmarks of someone trying to cram English into the model of some other language. Even if an academic grammarian HAS legitimately spotted such a beast, l even more skeptical that it does any good to learn about it. If this is really about the word "should," native English speakers just consider "should" to be a WORD, with a meaning, and with usage customs. "Should/would," "shall/will," "can/may" etc. we simply learn these as usage issues. And then half the time we ignore them. We express degrees of certainty, belief, wishes, etc. by our choices of words IN THE SENTENCE AS A WHOLE, we don't listen for whether the speaker said "shall" or "will." (British speakers pay more attention than U.S. speakers). Finally, you might want to read the usage note at https://ahdictionary.com/word/search.html?q=should You won't like it! It begins "Just as they ignore the traditional rules governing the use of shall and will, Americans largely ignore the traditional rules governing the use of should and would," and it ends "The best advice is to follow what sounds most natural!" Don't you hate that? The point is, you just have to pick it up from reading and speaking--formal grammar rules aren't going to help you.

Oblique Moods are taught at Ukrainian, Russian, Armenian pedagogical universities (!! you see how serious it is) for those students who want to be English teachers. I've neber heard about coursebooks by American or English writers with Oblique Mood devision (the Conditional Mood, the Suppositional Mood, Subjunctive I and Subjunctive II). But there are a lot of coursebooks of Soviet authors with this devision: 1. Blokh M.Y. A Course in Theoretical English Grammar. - M.: Vyssaja Sckola, 1983. 2. Ilyish, B. The Structure of Modern English. – M.: Prosveshcheniye, 1974 3. Gordon, E.M. A Grammar of Present-Day English / E.M. Gordon, I.P. Krylova. -2-nd ed., rev. and enlarged. M.: Vyssaja skola, 1980. - 335 p. 4. Ganshina, M.A. English Grammar / M.A. Ganshina, N.M. Vasilevskaya. 9th ed., rev. - M.: Higher School Publishing House, 1964. - 548 p. 5. Смирницкий А.И. Морфология английского языка. М., 1959. 6. Raevskaya N.M. Modern English Grammar. – Kiev, 1976. 7. Жилко Н. М, Панова Л. С. Практична граматика англійської мови: Навч. посібник для 2-го курсу ф-ту іноземних мов Me, myself I wonder is there any coursebook of English, American or Australian autors which mention Oblique Moods (the Conditional Mood, the Suppositional Mood, Subjunctive I and Subjunctive II)