Regarding official monographs; every single API can be analyzed by titration methods. Is it possible to analyze each API alone with its own official method with the presence of the other APIs or this may lead to error in the analysis.
It'll be difficult as well as time consuming to get precise result without AAS for metal ions determination, but you can use ion exchange HPLC (IE-HPLC) or Capillary electrophoresis using conductomeric detection as a possible alternative. Moreover, complexometric titration using masking agent could be an option for the quantitation of metal ions.