Acid tests narrow down the identity very nicely.
HCl test first. Anything that dissolves in HCl alone isn't a PM. You need to let it sit for a few days to a week to get some of the base metals to react. Steel and kovar won't react much or at all in concentrated HCl. Some water must be present in the solution. Add some copper chloride to get it moving faster (AP reaction) with parts that might have brass-copper. Wash remaining metal very well several times with warm distilled water (to get rid of all soluble chlorides) and then test with 50% nitric. Silver and palladium will dissolve in nitric. Take the solution from any leftover solids and add a drop of HCl or concentrated salt water to the filtered solution. If you get a fluffy cloud of white precipitate the instant the salt or HCl hits the solution, that's silver chloride. If there's no silver, test with stannous chloride for palladium (if it looks positive, dark black-green, test also with DMG for an absolute positive confirmation). If there is silver, drop all of it with salt water/HCl. Keep adding salt water/HCl to excess, then let the solid silver chloride settle out. You can then test the solution for palladium.
Metals remaining untouched after 50% nitric are much more likely gold and platinum (and mayyyyyybe rhodium, but that's not something you come across too often). There are some other resistant alloys, but they're not too commonly used. Use aqua regia next. If nothing dissolves in the cold aqua regia, carefully heat it. Platinum will dissolve only in warm/hot aqua regia. Then do a stannous test on the solution, being very careful as dissolved platinum salts are very toxic. So are palladium salts, by the way. Gold and silver salts have low toxicity, by comparison.
If you have metals STILL undissolved after warm aqua regia, then you could have iridium or rhodium. You could come across those metals with some old high-end tech, military stuff, laboratory equipment... and oddly enough, the nose-pieces of very old reading glasses! Because these metals react with almost nothing, the little nose clips of glasses from the late 19th century and early 20th were often made of a corrosion-resistant PM. This was an early practical use for platinum, rhodium, and even iridium with very expensive glasses (if the glasses have gold frames, then the metal parts of the nose pieces will likely be a platinum-group metal.)
I have some of those little nose pieces, and they pass through aqua regia as if it was just water! Obviously you'd need a LOT of antique glasses to get even a few grams of PGMs this way. I just keep them as curiosity pieces, and to compare with unknown metals in aqua regia.