Since SM3 and TASM 2, people are going to be very sensitive to the idea of more than one villain. The constant with those two movies is that they all showed up shoehorned in the finale together. I'd be all for having 3 villains in the next Spidey reboot, if they do it properly.
Have the main villain, then have two side villains. One that he fights towards the beginning as he's developing his powers. (Shocker for example) He doesn't even need an origin, just have him robbing a bank with his suit on. No explination, he's just there being Shocker because he's Shocker. Just DON'T include him in the finale! Once he's defeated, he's done, off to Ravencroft. Then you have your main baddie throughout the movie and one more baddie at the end. (Rhino TASM 2 style)
The problem TASM 2 and SM3 made was linking the villains. Sandman Venom teamup, Dane DeForhead and Electro team up. The side villains in the new reboot should be completely on their own for the own motives. Shocker at the beginning, maybe a hint or easter egg of the Vulture or Doc Ock at the end.
What I'm saying is having more than one villain WILL work for a reboot. Just don't connect the villains with shoehorned plot lines. That's what ruined SM3 and TASM 2.