Chemistry - How to identify an emerald green solution with possibly two anions?

You can have two different anions if your solution is a mixture of two different metal salts, a chloride and a sulfate. The color change from green to blue upon dilution with water fits well with $\ce{Cu^2+}$ being the corresponding cation. Concentrated solutions of $\ce{CuCl2}$ are green due to the presence of chlorocuprates, like $\ce{[CuCl3]^{-}}$ and $\ce{[CuCl4]^{2-}}$. When water is added, a stepwise ligand exchange takes place, and the pale blue color of $\ce{[Cu(H2O)6]^{2+}}$ starts to appear. The image below shows copper(II) chloride solutions of different concentrations: Green when the chloride concentration is high, and blue when it is lower (Wikipedia: copper chloride).

In summary, the observations (color change, precipitates) indicate that you have an aqueous solution of $\ce{CuCl2}$ and $\ce{CuSO4}$.