Yes, simple duplication does not work for some things as there are far too many connections to deal with, etc.

Since you simply need the same type of particle and emitter settings, all you need to do is get your first emitter and particleShape acting and looking the way you want, then:

1. Open the attribute editor for your emitter.
2. At the top-right of the Attribute Editor dialog window, there is a "Presets" button.
3. Click and HOLD that button to create a preset for your current emitter settings.
4. Now, select your ParticleShape and follow steps 1-3 again.

Now, all you have to do is animate any more spheres you need, then simply apply a surface emitter to them, and apply your "Preset" you created earlier by opening the attribute editor for the NEW emitters and particleShapes, and holding-down the Preset button, and choosing "Replace"

Good luck!