6 string bass setup (truss rod)

[Riccardo90]

Hello there!
I recently got myself a cheap 6 strings bass, mostly out of curiosity. The previous owner had tightened the truss rod quite a lot, as a result the bass had a nice low action but some problems with the frets (mostly if I tried tapping the string would hit quite loudly against the frets between my finger and the nut). So I decided to try to fix the set up myself (first time I play with the truss rod). I gradually loosened the truss rod until the neck seemed to have the proper relief (hold the lowest string at 1st and last fret and you should have a space of about a credit card at the 12th fret), I lowered the action as far as the bridge allows me and I now have nearly 4mm between the 12th fret and the low B string. However, a few problems showed up:
-the 4th fret of the high C string started to buzz quite a lot
-the 21st frets of the high C sounds like the 22nd (the same happens for other frets around the 17+ area for the G and D string)
-the three lowest strings start buzzing from the 12th fret on and soon they just don't play because they hit the higher frets (as if the neck stopped having relief around fret 15)
As I was saying I am quite new to these operations and I am not sure what is the origin of the problem, I could try to loosen the truss rod even more but I am afraid that is going to be just too much, and rising the action would soon make the bass not really playable.
Does anybody have an idea what might be going on here?
Any type of suggestion is welcome, I am already in the learning mind set
Thanks a lot and sorry for the long post

P.S.
If it helps, this is a HK bass, but I don't know the model so I can't really give the specs

 

[Turnaround]

You need to review the specs for a setup. For example, a credit card’s amount if relief is about 3 times what it should be. It should be a business card thickness. With that much relief you run the risk of notes choking is the upper registers if you use lowish action.

Check the stickies at the top of the forum for guidance in setup.

 

[Riccardo90]

You need to review the specs for a setup. For example, a credit card’s amount if relief is about 3 times what it should be. It should be a business card thickness. With that much relief you run the risk of notes choking is the upper registers if you use lowish action.

Check the stickies at the top of the forum for guidance in setup.

Oh I see! So probably I already have too much relief and that's my problem!
I kept loosing the truss rod because I kept having either a problem with tapping or problems with buzzing frets, but probably I just missed the sweet spot in between.
Somehow online I couldn't find much on what are the consequences of a too loose truss rod (beside high action).
Thanks a lot!