I have thought a lot about the problem (worked as a professional bassoon player for a very long time), and I can't say I have had many good ideas. There are some ideas for simplified music notation (with different shapes for flats and sharps) which work _very_ well for making sight reading easier. Until it doesn't: It can't express enharmonics (different ways of writing the same note), which makes tonality analysis harder, and can actually hamper readability since most people that are fluent in reading music usually "stay in key" when reading music.
A quick google gave me this: http://musicnotation.org/ and I can't say I am very impressed by anything I see there. But as you notice, most systems are oriented by lines. I don't think that is because people lack fantasy, but because it is a pretty good way to write music.
If you drop that requirement (and then assume digital storage) you could have 1. an underlying canonical format that has "all the information" but which is never presented to the performer, nor to the composer; and 2. a number of views that expose various dimensions of the composition. Like orthographic projections of a model in CAD software.
Presuming an interactive display (touchscreen, etc.) you could switch between these views at will; but even for printed sheet music, you could just isolate one measure at a time and then display several "stacked" views of that measure per page.
(Basically, picture widely-spaced, annotated sheet music, but where the annotations are themselves in the form of more musical notation, rather than words, appearing in additional sub-staffs attached to the measure.)
I don't believe this to be true. (Modern) Guitar Music is most often written in tab often without accompanying staff notation. Also staff notation is not loseless, musicians will interpret the music differently. For example, with violin, whilst some instruction is given on bowing it is almost never complete and the musicians will find different ways to fit the bowing to the rhythm, this can make a huge different to overall tone as (most simply) the up bow sounds distinctly different to the down bow.
Conductors can write notes about certain parts that can be accessed by musicians. Opera musicians (where different people play the same music every night) can have their own personal notes.
Most exciting is ofcourse that everyone has instant score access. That removes a shit-tonne of time wasted during rehearsals.
Those are just traditional use cases. I'm excited to see what will come. I don't know ifusic as it is practicedtoday can be "expanded" in any meaningful way, but that only time will tell
I've got a plan on the backburner to do something like this using Ohm https://ohmlang.github.io/