here are some notes on how to test metals:
Each metal/alloy has its own set of procedures known to work best. First step it to dissolve the sample. How depends on the composition.
More methods exist outside the chemistry lab. There is an instrument that creates sparks with the alloy and analyzes the spectrum, for instance.
Depending on need, there may be problems with some elements: carbon, silicon, boron, nitrogen - these two being intentional and very active in 0.1% concentration -, phosphorous... absolutely necessary to measure in most steels.
Normally, density (which is easily measured to 10-3 accuracy on a simple shape) gives you the main element and the main alloying element including its proportion.
Most analysis methods are incapable of measuring some of the elements present in the alloy. Dissolving in acid won't show the nitrogen contents, probably not the phosphorus nor silicon, and so on. Sparks-and-spectrum can't properly show light elements.
Some elements are desired in some steel, even in small amounts, like nitrogen in Duplex 2205 or boron in some turbine refractory steel.
Other elements are very detrimental, hence not intentional, and must be measured. Phosphorus makes steel brittle even in small amounts. So does carbon, which is why it is added.
Some alloys specify a very low guaranteed maximum of some elements, like 0.02% carbon in many stainless steels.