Instead of dividing a beat, or an entire sequence of beats, could it be that it alters the duration of (say) one and a half beats?
Yes, absolutely. For a typical "three in the time of two" tuplet (a triplet), just select the note length that will give you half of the length you desire. So for 4/4, one beat is a quarter and 1.5 is a dotted quarter; half of that is a dotted eighth.
Here's an example I made in Finale to represent that:
You can see that the dotted-eighth tuplet takes up the same time as the dotted quarter — 1.5 beats.
As rightly noted below, that contrived example could be expressed without triplets and only serves to confuse the notation. However, there are cases where it is more useful — when the fractions don't work out so neatly. For example, 5 in the time of 3:
(Note that the notation could probably be clearer so that you don't have to look at the remainder of the bar to figure out how much time that tuplet takes up.)
In "traditional" notation, tuplets only occupy a complete number of beats, or a simple fraction (e.g. 1/2, 1/4) of a beat.
In "contemporary classical" music, you can write whatever you want to define the rhythm - but as another answer says, your example is pointless since the notes in the tuplet are the same length as ordinary 8th-notes.
It may be clearer to label the tuplet as a ratio like "7:5" or even as "7 eighths : 5 quarters" (using symbols rather than the words "eighths" and "quarters" - most notation software has an option to do that)
You can also nest tuplets inside each other, so for example a "7:5" tuplet might actually consist of 2 of the 7 notes, then a nested "3:4" tuplet and finally the last note of the 7 - but whether the performer is expected to play such rhythms with mathematical accuracy or not is another issue.
You can even write tuplets that cross bar lines - though some notation software can't handle that yet, even though I have a published score (composer Scriabin) using that notation more than 100 years ago.
Might need a more concrete example of the kind of thing you're asking. But if you mean: can you do something like a quaver triplet on beat one and a semiquaver triplet and quaver rest on beat 2 in common time, yes, absolutely. But making 1.5 beats into a triplet is just three straight (non-triplet) quavers, so in that sense - no.