Agreed, it looks like a Paramount with some braze-ons added before a repaint. No chance it ever had the serial number stamped on a head badge as that only happened on Japanese built frames. If it was in fact a chrome Paramount it would have looked something like this when new. You won’t want to let it hit scrap yard, Paramounts are quite nice and a worthy project if you’re so inclined.
Serial number should be located here but you never know if a new dropout was brazed on at some point. As Juvela says check the stearer tube, the number should be stamped there as well.