Coloring comments is generally handled by font-lock referring to the mode's syntax table, this only supports one face for comments.
You can however, specify a regexp for font-lock to force highlight in any color you want, this way we can specify a regexp that matches "//" followed by text, followed by "||" followed by more text, and have font-lock highlight the "||" and the following text only.
Here is a basic implementation of this in a major mode.
;; your custom face to color secondary comments blue
(defface my-second-comment-face '((t (:foreground "blue"))) "its a face")
(define-derived-mode testy-mode fundamental-mode
"test"
(modify-syntax-entry ?/ "<1")
(modify-syntax-entry ?/ "<2")
(modify-syntax-entry 10 ">")
(font-lock-add-keywords
'testy-mode
;; this highlights || followed by anything to the end of the line as long as there is
;; a // before it on the same line.
;; the 2 means only highlight the second regexp group, and the t means highlight it
;; even if it has been highlighted already, which is should have been.
'(("\\(//.*\\)\\(||.*$\\)" 2 'my-second-comment-face t))))
You should note that this is a basic solution that doesn't handle all cases. A normal case like
foobar // comment || more comments
will be handled correctly, but something like
foobar "string//string" || text
will not work correctly, the || text
will be highlighted even though // occurs in a string

If you want fontification of these secondary comments to be "smarter" you will need to look into more advanced techniques for fontification. You use a hook in jit-lock-functions
to do this. In your jit lock function, you would need to scan for the ||text pattern and highlight it based on whether or not it is already in a comment which you can find out with syntax-ppss
assuming your syntax table is set up correctly.