Lets assume we have copper and silver as an soluble alkaline amine solution,
Ag(NH3)2 + Cl- and Cu(NH3)4Cl2
Adding HCl Acid we precipitate silver from the solution, as silver chloride AgCl solid powder, in an ammonium chloride solution.
Ag(NH3)2Cl- + 2HCl --> AgCl(s) + 2NH4Cl (aq)
This removes the silver compound that posed the solutions danger if concentrated with heat or dried...
Removing our silver chloride powder for processing later to make silver metal with other chemical reactions.
Copper amine in solution follows a similar reaction with the acid, but no precipitant occurs as both products are soluble copper chloride and ammonium chloride.
Cu(NH3)4Cl2 + 4HCl --> CuCl2(aq) + 2NH4Cl(aq)
Just a little excess acid here wont hurt and can be benificial.
Now if we add iron metal ( to this acidic solution) we can cement or displace the copper from solution, removing copper from the solution leaving us with an iron chloride (mixed with our ammonium chloride),
CuCl2(aq) + Fe(s) --> Cu(s) + FeCl2(aq)
letting the copper settle and decanting the solution, leaving us with an iron chloride and ammonium chloride solution, adding sodium hydroxide we can now raise the pH (around pH9), and precipitate the iron (and most any other base metals the may have been involved) removing iron and base metals from solution as insoluble powder hydroxides, then after decanting the caustic solution from the powders, we can add enough acid to bring the pH to neutral (pH7) we are left with a neutral solution of sodium chloride and ammonium chloride salt water which can be evaporated safely or disposed of in a safe manner.
Basically after removing your silver you treat this waste like you would do your other waste.
just treat it separately from your other acidic waste solutions.