Souls have being split into multiple halves many times in the series. Some examples being Kuruma, Minato, Kushina, Hagoromo (He gave Naruto and Sasuke seals separately) and Orochimaru.
I doubt the firepower would decrease with access to an unlimited supply of chakra. Plus when souls split they regenerate to thier originals (Best example being Kuruma).
So, yeah it is possible. It just makes Edo Tensei even more broken then it already is.
- Kurama is just a lump of chakra meat; doesn't have a soul.
- Minato and Kushina never split their souls; they just planted their remaining chakra inside the seal and used it in a similar manner to Edo Tensei, to summon their conciousness at the right times.
- Giving your chakra is not splitting your soul;
chakra and the soul are two different things.
- Orochimaru was revived, not had his soul split. His soul was basically reborn by combining the consciousness residing within Anko and tying into flesh.
This isn't Harry Potter; souls don't get split so no, it's not possible. You live with one soul and once you die, it goes to the Pure Land. Only by using Edo Tensei or Rinnegan's Outer Path can it be summoned back.