How many chains is too many? Usually three, sometimes four if two of them are fine and one is doing something interesting. Beyond that you're not layering, you're wearing a curtain, and it stops looking deliberate.
The difference between a layered set that looks put together and one that looks like a drawer emptied onto your neck comes down to chain weight and length spacing. Each strand needs its own job: a short one sitting close to the collarbone, a middle length that clears the neckline of most tops, and a longer one doing the dramatic bit lower down. If they're all bunched within a couple of centimetres of each other they'll tangle constantly and sit as one messy clump rather than three distinct lines. Good ones use slightly different chain styles too, a fine cable chain against a flatter curb link against something with a bit of texture like a bead or a disc, so your eye can actually separate the layers instead of seeing one blurred mass of gold. Cheap sets tend to use identical thin chains at similar lengths, which is why they knot themselves into a ball in your jewellery box within a week. Check the clasps as well. A lobster clasp that's actually easy to work one handed matters more than it sounds, because you will be doing this with wet hair and no mirror more often than you'd like. Plated finishes wear thin at the clasp and the parts that touch your skin first, so look for something stating the base metal, and be wary if there's no mention of it at all.
These work best doing the job a single pendant can't, which is filling out a neckline that would otherwise look bare without shouting about it. A plain crew neck jumper or a simple shirt with the top buttons open is the right stage, nothing with its own pattern or heavy collar detail competing for attention. They're a cold weather piece in some ways, since a jumper gives the shortest chain something to rest against rather than sliding around on bare skin, but they also do well over a slip dress in summer when you want something at the neck without the formality of one statement piece. Before buying, check how the chains attach if they come joined at one point, because a bad join twists itself into knots within a day, whereas separate chains worn together behave far better and let you drop one out whenever you fancy a simpler look.
The genuinely good ones sit so differently in weight that you can feel which chain is which with your eyes shut, and that's the whole point of buying layers rather than one necklace that tries to do three jobs badly.