According to http://web2.uvcs.uvic.ca/elc/studyzone/410/grammar/410-modals-of-possibility-and-probability-with-continuous-tenses.htm, modal verbs+ ing could be used in the following formulas:
modal verb + b + ing
Person A: What's that noise?
Person B: Oh, that's just my brother's band, they must be practicing.
APPROPRIATE MODAL + HAVE BEEN + ING
Also:
Must, could, might, may, couldn’t, can’t, may not and might not are used to show how certain the speaker is that an action is presently occurring or not occurring. Using must conveys a strong feeling of certainty; nevertheless, there is still some doubt in the speaker’s mind.
Could, may and might show that a speaker is 50% or less certain that an action is in progress.
Couldn’t and can’t show that the speaker believes strongly that a situation is not taking place. For example:
It’s noon. George went to bed at 10:00 last night. He can’t still be sleeping!
May not and might not convey the idea that a speaker is 50% or less certain that an action is not possible or probable. They are not normally used in their contracted forms.
Correct: They aren’t here yet and it’s getting late. They might not be coming.
Incorrect: They aren’t here yet, and it’s getting late. They mightn’t be coming.
Might and could are used in questions regarding the possibility or probability of actions taking place. However, may and must are not.
Correct: Could Tom be studying now?
Incorrect: May Tom be studying now?
For most short answers, a modal alone is used. However, if the question includes a be verb, a modal with be is required.
Person A: Is Simon joining us?
Person B: I’m not sure. He might be.
Remember that not all verbs are used in the continuous (progressive) form. Non-action verbs that describe situations or conditions that aren’t expected to change, such as seem, appear, cost, weigh, have and be are not used. Other types of non-continuous verbs are:
Verbs of the senses (hear, smell, see, taste, etc.)
Verbs of ownership (have, belong, own, possess)
Verbs that convey feelings (love, hate, like, hate, prefer, want, etc.
1The first one, *would constantly be teaching* is completely "natural", because of the meaning - the "teaching" is a repeated / extended action, reflected by the modal *would* and continuous *teaching* (note that *would be constantly teaching* is a perfectly valid alternative). Although it's grammatical, the second would be extremely unlikely in isolation, but again it's completely natural in context (since it just echoes the form already used for those past situations in respect of the father). – FumbleFingers Reinstate Monica – 2016-03-30T11:57:50.860
would there is past-tense of "will". – Tᴚoɯɐuo – 2016-03-30T12:07:04.007
1Consider: "I really need my own room, dad. I'll be sittin' there, tryin' to read, and Johnny'll come in and start playing a loud FPS video game. Now that I'm entering high school, I'll be wanting to buckle down, but he'll constantly be making it impossible for me to get any work done if I don't have my own room." – Tᴚoɯɐuo – 2016-03-30T12:15:21.800
1"I really needed my own room. I'd be sittin' there, tryin' to read, and Johnny'd come in and start playing a loud FPS video game. Now that I was entering high school, I'd be wanting to buckle down, but he'd constantly be making it impossible for me to get any work done..." – Tᴚoɯɐuo – 2016-03-30T12:20:34.807