Once you move beyond 7ths and start adding notes from higher up the scale (e.g. 9ths, 11ths, 13ths) there is one very important thing to remember.
All of these chords must have a 7th in them.
Just as there are 3 types of 7th chord (7th, min 7th, maj 7th), you end up with 3 types for 9th, 11th and 13th chords by simply adding to the basic 7th chord.
To get a 9th chord, add the 9th to the (flat) 7th chord
To get a min 9th, add the 9th to the min 7th chord
To get a maj 9th, add the 9th to the maj 7th chord
To get 11th chords you can add the 11th to the 3 types of 9th chord, but most of the time the 9th is not needed, so you simply add an 11th to the 7th chords to build the 3 types of 11th chord, and similarly with 13ths.
If you have a voicing of a 13th chord that also has a 9th or 11th in it, then that's fine: it's still a 13th chord, but most of the time these chords are just a normal 7th with an added note (9th, 11th or 13th)
9th, 11th, and 13th Chords
The spelling for chords like C9, C11, C13 (i.e. chords built on C7 - so they have a flat 7th in them) is:
9th: 1st, maj 3rd, 5th, flat 7th, 9th
11th: 1st, maj 3rd, 5th, flat 7th, 11th
13th: 1st, maj 3rd, 5th, flat 7th, 13th
It's worth noting here that the 5th can be omitted from the chord. The essential notes for C9, C11 and C13 are the 1st, 3rd, 7th and 9th/11th/13th