If substitution values differ only in the numbers at the ends, use the command
:let n=[0] | %s/|/\='new'.map(n,'v:val+1')[0]/g
(See my answer to the question "gVim find/replace with counter" for
detailed description of the technique.)
In case of substitution values that differ essentially from each other, change
the command to substitute not a serial number of an occurrence, but an item of
a replacement list with that number as an index.
:let n=[-1] | %s/|/\=['one','two','three'][map(n,'v:val+1')[0]]/g
To perform the substitutions on every line independently of each other, use
the :global
command to iterate one of the above commands through the lines
of a buffer.
:g/^/let n=[0] | s/|/\='new'.map(n,'v:val+1')[0]/g
Similarly,
:g/^/let n=[-1] | s/|/\=['one','two','three'][map(n,'v:val+1')[0]]/g