I'm afraid not.
This is actually a ‘fossilized’ expression with a long and complex history, summarized by OED 1 as follows: In the idiomatic I, we, you, he, etc.
had better , the original construction was me, us, etc. were betere (or bet )
= it would be more advantageous for me, etc.
[...] The dat.
pronoun was subsequently changed into the nominative,
I, we, were better (perh.
because in sbs.
the two cases were no longer distinguished).
Finally this was given up for
the current I had better =
I should have or hold it better, to do, etc.
(Mr. F. Hall has shown that in these changes better followed in the main the analogy of liefer and rather .)
†
It is really pretty hopeless to try to force this idiom into the straitjacket of conventional syntax, much less try to rephrase it with conventional transformations.
It is what it is.
†
Mr. F. Hall is the 19th-century philologist Fitzedward Hall , an obsessive scholar of whom the OED ’s first editor wrote that ‘When the Dictionary is finished, no man will have contributed to its illustrative wealth so much as Fitzward Hall’.
His essay ‘On the Origin of “Had Rather Go” and Analogous or Apparently Analogous Locutions” , American Journal of Philology , II.7 (1881) is delightful reading, not merely for the substance and copious documentation but chiefly for its wickedly acid remarks on attempts by earlier grammarians to make sense of this construction.
ell.stackexchange.com/users/32/StoneyB on hiatus
Did you mean to change it to a question, or to ask if the following is sensible?
I'd be better to get a quart.
If you said that to me I could respond by making a quizzical face and say: "I'd be better to get a quart?
"
(...as a challenge to the fact that I didn't understand what you just said, because it sounds weird.)
Yet it could pass for old-timey pirate language, as a sort of short-hand for "
I'd be better off if I were to get a quart.
"
first mate: "Cap'N,
would you like me fetch ye a gallon of skunk whiskey?"
cap'n:
"Arrr, nay!
I'd be better to get a quart of yonder Basil Hayden.
"
If you spoke like that people would know what you mean (and that you were a pirate).
But it's not normal speech, and you should go with
"I'd better get a quart." ...
assuming you live in a place where people know what quarts are.
ell.stackexchange.com/users/9598/HostileFork says dont trust SE
I agree with HostileFork, especially the pirate comment, but if you feel a burning desire to use "be better" you would say: It would be better to get a quart.
That is, it would be better {for me and all concerned} to get a quart.
Someone who knows how much your friends like to drink might say: You would do well to get a quart, not a pint.
ell.stackexchange.com/users/10264/Tᴚoɯɐuo
"I’d be better to get a quart" does not sound natural to my (American) ear.
"I'd be better off getting a quart" does sound natural to me.
In both of these examples, "I'd" is short for "I would".
ell.stackexchange.com/users/9100/Jasper
There's a bit of difference in meaning between the 2, and I don't think the 2nd is something you'd be likely to hear.
I'd better get a quart.
It's preferable that I get a quart under the given circumstances (whatever they happen to be).
This may prevent some unforeseen negative consequence in the future that could affect anybody.
I’d be better to get a quart.
It would personally improve me and make me better if I got a quart.
This version doesn't really make sense and sounds incorrect.
I’d be better off getting a quart.
I'd do better to get a quart.
These are both equally acceptable options, though again the focus shifts from the situation to the speaker.
I'd be better off with a quart because of the positive outcome for me, or the aversion of a negative outcome for me personally.
ell.stackexchange.com/users/8285/mc01
I' d better  get a quart. ( daum.net )   There’s a  had better  usage in the above. I’m not trying to figure out what the original it would have been, but can this construction below be made? (When  I , the main verb, is logically the object of the non-finite verb -  get , it could be thought as a  tough movement . But it's not the case.)    I’d be better to get a quart.
I'd better get a quart
ell.stackexchange.com
<infinitives><semi-modals>
ell.stackexchange.com/questions/34090
ell.stackexchange.com/users/504/Listenever
I’d be better to get a quart does not sound natural.  There's a bit of difference in meaning between the 2, and I don't think the 2nd is something you'd be likely to hear. It is really pretty hopeless to try to force this idiom into the straitjacket of conventional syntax, much less try to rephrase it with conventional transformations. This idiom does not fit with conventional syntax, the two differ slightly.
This idiom does not fit with conventional syntax, the two differ slightly.