So, just as the question states, what if Voldemort had thought ahead enough to put pieces of his soul into other bodies? In this way, wouldn't there simply be more than one Voldemorts at any given time?
Also, what if Voldemort never had a helper in order to assist him in returning? Then he would just a miserable fragment of a soul, wondering around. The horcruxes would guarantee him life but he would be only barely that.
As discussed in comments, @jason-baker is right. If a living being is a horcrux, and that person dies, so does the horcrux. You may ask why this is - why does the horcrux not just occupy the dead body? The reason is the same as the reason why the horcrux is destroyed by the Sword of Gryffindor even though there is still a locket (albeit a damaged one). Horcruxes are living things and can die by weapons powerful enough to irreversibly damage the body. A flesh body is presumably not able to be protected from destruction like a Horcrux can otherwise everyone would make themselves practically indestructible, especially against the Avada Kedavra curse which I can't imagine hurting an inanimate horcrux.
Putting a horcrux into a dead body would not suggest the horcrux could possess the body - none of the other horcruxes developed the ability to move (then again they did not have muscles with the exception of Harry, and Nagini who were both still alive)
Finally, putting a horcrux into a living body does not cause that person to become Voldemort - Harry did not become Voldemort, although at times he reflected Voldemort's feelings. And Nagini presumably, did not have the mind of Voldemort either (although it has been noted by Dumbledore that his snake was unusually loyal, and perhaps this is why). This is based on the time when Harry in a dream saw through the eyes of Nagini in Half-Blood Prince - Harry shared Nagini's thoughts, which were different to Voldemorts, more snake like (in my opinion).
So Voldemort could not have created more Voldemorts using horcruxes.
UPDATE: Even if he could have done so, he would not have. Voldemort was incredibly narcissistic and determined to be the greatest wizard of all time, unique, something of legend. He can't do that if he's got copies of himself running around. He would not have allowed himself to become something ordinary/non-unique. That is probably why he didn't make his Death Eaters drink polyjuice potion all the time so that no-one would know whom to target, as Harry did when trying to escape, which arguably would have been more terrifying.
In chapter 23 of Half-Blood Prince, Dumbledore answers this (emphasis mine):
"The snake [Nagini - obviously]?" said Harry, startled. "You can use animals as Horcruxes?"
"Well it is inadvisable to do so," said Dumbledore, "because to confide a part of your soul to something that can think and move for itself is obviously a very risky business. However, if my calculations are correct, Voldemort was still at least one Horcrux short of his goal of six when he entered your parents' house with the intention of killing you. [...] I am sure that he was intending to make his final Horcrux with your death. As we know, he failed. After an interval of some years, however, he used Nagini to kill an old Muggle man, and it might then have occurred to him to turn her into his last Horcrux. She underlines the Slytherin connection, which enhances Lord Voldemorts mystique; I think he is perhaps as fond of her as he can be of anything; he certainly likes to keep her close, and he seems to have an unusual amount of control over her, even for a Parselmouth."
It makes sense to not use a living thing as a Horcrux: as we've seen with Harry (and also Nagini), all it takes to destroy one is to kill it, and something that can walk around on its own could accidentally kill itself in any number of ways.
Voldemort only resorts to this when he has very few other options. Nagini, for example, is the last Horcrux he creates, as confirmed in a 2007 live chat on the Bloomsbury website:
Lady Bella: Whose murders did voldemor [sic] use to create each of the horcruxes
J.K. Rowling: The diary - Moaning Myrtle. The cup - Hepzibah Smith, the previous owner. The locket - a Muggle tramp. Nagini - Bertha Jorkins (Voldemort could use a wand once he regained a rudimentary body, as long as the victim was subdued).
J.K. Rowling: The diadem - an Albanian peasant. The ring - Tom Riddle snr.
We can speculate, as Dumbledore does in the HBP quote above, that Nagini was turned into a Horcrux because Voldemort, recently returned to a physical body (albeit a weak one), desperately wanted to complete his "seven Horcrux" spell. Nagini was a relatively safe choice for a "vessel" because of Voldemort's level of control over her and because, especially at this stage of Voldemort's life, she's never far away.
At any other time in his life, it would have been too risky.
