There are what I might, for now, unscientifically call “gaps” in language, in the sense that certain pieces of a particular pattern in a grammar are missing, and are not replaced/suppleted by anything else. In this sense, the absences of, say, goed or goodest are not gaps since they’re suppleted by went and best, respectively.
Likewise, the absence of a future or infinitive modal can, as in (3) and (4), is perhaps not a gap since we can reformulate the idea with (be) able to, as in (5) and (6), and can and (be) able to are pretty synonymous, I think.
(1) Harold can recite 1,000 digits of pi, but not necessarily in order.
(2) When he was 12, Harold could recite 1,000 digits …
(3) *By next year, Harold will can recite 1,000 digits …
(4) *Harold hopes to can recite 1,000 digits …
(5) By next year, Harold will be able to recite 1,000 digits …
(6) Harold hopes to be able to recite 1,000 digits …
An example of what I’d consider a gap, and quite a frustrating one sometimes, is the absence of many forms of be supposed to that one would possibly think ought to be okay. The one that always gets me is the past perfect, as in (9) and (10).
(7) My landlord is supposed to fix the door.
(8) My landlord was supposed to fix the door 3 weeks ago.
(9) *My landlord has been supposed to fix the door for 3 weeks.
(10) *It’s been 3 weeks since my landlord has been supposed to fix the door.
According to a very technical and precise statistical analysis of about four or five people’s responses on Facebook, as well as a short discussion on WordReference, present perfect has been supposed to is ungrammatical.1 And the same goes for the infinitive, i.e. be supposed to preceded by to or a modal, as well as for the gerund.
(11) *My landlord claimed to be supposed to go out of town.
(12) *My landlord might/could/should/must/would be supposed to go out of town.
(13) *My landlord denied being supposed to fix the door.
But there’s a bit of weirdness when it comes to the subjunctive.
(14) If my landlord is supposed to fix the door tomorrow, then he’ll come around 8:00 AM.
(15) ?If my landlord had been supposed to fix the door yesterday, then he would’ve come around 8:00 AM.
(16) If my landlord were supposed to fix the door today, then he would be here by now.
(17) *I insisted that my landlord be supposed to fix the door today.2
Considering has been supposed to in (9) and (10) is bad, it’s strange that had been supposed to in (15) is relatively better, albeit still degraded compared to (14). That is, it’s not as good as (14), but oddly better than (9) and (10). Moreover, the past subjunctive were in (16) is perfectly fine, leading one to think that the present subjunctive be is fine too, but that’s not the case. (Thanks to entangledbank for these sentences.)
The reason I consider this a gap is because there really is no semantically equivalent alternative for supposed to like there is for can. The closest in my mind is probably have to, but there’s definitely a difference in meaning between the two, whereas there is no such difference (that I can perceive) between can and be able to in most contexts.
One explanation for some of the above facts might be that be supposed to is modal not only semantically, but also syntactically, just like can. That is, it (or at least the inflected part) is generated in/occupies the same syntactic position as words like can, might, to and would, hence why they cannot co-occur.
But that doesn’t explain why has been supposed to is bad. If is and was are acceptable inflections, why not has been? And why is subjunctive had been slightly better, but not perfect? And what’s wrong with the gerund?
It’s interesting that this use of supposed to also has a particular pronunciation to it, which contrasts with supposed to in the sense of “assumed to”, as in (18).
(18) The killer is supposed (by the authorities) to have fled the country by now.
Obligation supposed to is pronounced something like [səˈpoʊstə], with voiceless [s], whereas “assumed” supposed to is [səˈpoʊzd + tə (tu)] (two distinct words), with voiced [z], which of course makes sense since it’s the past participle of the verb suppose, which has [z], not [s]. Obligation supposed is arguably no longer really the participle of anything.
In a way, then, maybe obligation be supposed to has been re-analyzed/re-lexicalized. It’s similar to gonna, which in fact seems to have the same sort of distribution.
(19) My landlord is gonna fix the door.
(20) My landlord was gonna fix the door.
(21) If my landlord were gonna fix the door, …
(22) *If my landlord had been gonna fix the door, …
(23) *I insisted that my landlord be gonna fix the door.
(24) *My landlord claimed to be gonna fix the door.
(25) *My landlord might/could/should/must would be gonna fix the door.
(26) *My landlord denied being gonna fix the door.
Some (but not all) of the sentences of above actually get better, at least to me, with the unreduced going to in place of gonna, e.g. (27).
(27) ?My landlord claimed to be going to fix the door tomorrow.
Read with a future meaning, not a movement meaning, of course. With be supposed to, however, there is no such semantically equivalent unreduced version available.
1Note that I’m disregarding, for now, the use of supposed to in the sense of “assumed to”, as in (18).
2It’s entirely possible that (17) is bad for semantic reasons: it’s rather redundant. Unfortunately, I can’t think of any verbs/adjectives that take the subjunctive that aren’t verbs/adjectives of necessity/obligation, which be supposed to already conveys.