Possibilities #1: Comparatives on non-adjectives

Fun things with comparatives and superlatives

Superlatives and comparatives are not universal in human languages, c.f. Biblical Hebrew and such. Certainly there's ways of expressing whether something has more or less of some quality than something else, but there is not even any guarantee that this would be a set periphrastic construction - there may well be one, but it could also be the case that one can come up with any variety of ways of expressing it. 

How about using the same morphemes with verbs as well? This could lead to a variety of shifts in meaning:

• doing something more intensely, or with greater [whatever] than what usually characterizes the verb, e.g. run faster, shout louder, play more melodiously, play louder, preach convincingly, preach annoyingly, preach with even greater hypocrisy than usual, sleep tight, sleep such that it is difficult to wake the sleeper up, run fast, run clumsily/trample,  ...
• doing something to a greater number of objects (or indirect objects)
• doing something more often, more frequently, more deliberately, more intentionally, more ...
• ...

Adpositions obviously could be compared:

close to - closer to - closest to

above - higher above - on top of

It would be of some interest to maybe have fewer grammatical distinctions in the comparative or somewhat; as if positive and superlative adpositions form triplets distinguishing from - at - towards, whereas the comparatives are defective in lacking the distinction between at and towards?

Finally, for nouns, one could easily obtain meanings like

• greater importance
• greater stature
• greater size in general
• greater in some essential quality (harder stone, etc)

The important thing I would go for with a system like this is not any kind of unified meaning - not just picking one and using that for the entire noun system or even locking every specific noun to its preferred alternative. Rather, some nouns or verbs may favor just one of them for the majority of use - so like, 95% of the use of house.comparative would relate to size, whereas a similar percentage of house.superlative might refer to some kind of religious building, functionally important building or otherwise remarkable building.

That is, it should be very contextual rather than fixed.

[EDIT:

Finally, in Finnish, comparatives sometimes go on nouns with locative endings, indicating 'closer to'.)