Question: When I did `git stash push <path/to/file>` it created `stash@{0}` for it.
Reusing the same command with different file creates another stash -> `stash@{1}`.
I have other files that logically belong to stash@{0}. 

Can I somehow push file to existing stash?

Answer: 
If you mean akin to `git commit --amend`, I am afraid you are out of luck, but would it be acceptable for your use case, to:

`git stash pop`

and then

`git stash push ORIGINAL_FILES MORE_FILES`

to have the files grouped?
As per git [docs](https://git-scm.com/docs/git-stash#Documentation/git-stash.txt-ltstashgt),

> 
> `<stash>` 
> 
> 
> This option is only valid for apply, branch, drop, pop, show
>  commands.
> 
> 
> A reference of the form `stash@{<revision>}`. When no `<stash>` is given,
>  the latest stash is assumed (that is, `stash@{0}`).
> 
> 
> 

So you can't do this directly using `push` command of `git stash`.

Probably use this `git stash push <path/to/file1> <path/to/file2> ...` next time as `push` accepts multiple pathspecs (filenames)