What procedure could be used for separating the metal ions by precipitation?
You need to look at your tables of solubility. You’re not going to want to add other metal ions, except possibly alkali metal ions like sodium or potassium that are almost impossible to precipitate. Concentrate on the anion. Especially think of things like chloride, sulfide, carbonate, hydroxide. Also, think about pH. Some metal chlorides, for example, will precipitate in acid solution. Others are very soluble. Hydroxides will, obviously, not precipitate in acidic solution, but might precipitate in weakly basic or strongly basic solutions. Bubbling hydrogen sulfide into solutions is a classic method of performing qualitative analysis. Some sulfides will precipitate in acidic solution. Others will not precipitate until the solution becomes basic. Since the vat contains a solution, it presumably is a solution in water. Here are some solubility rules that will help you.