Tandem wifi will it work as planned?

I have a wireless network setup in my house and it's starting to work rather well however when I get into the distant sections of my house the wireless signal drops off significantly. I have researched a couple of ideas to solve this one idea that I am liking the best so far is to set up multiple wireless routers in tandem, I have seen the range extenders however that still seems to me like the system would be still limited by the speed of one router so I have thought the best idea is to run multiple routers in tandem! My idea is that I can run wires to a couple of spots in my home then use a wired router that should be faster to split the signal to multiple wireless routers to conserve the speed and bandwith my question is with a setup like this can I set all of the routers on the same signal and create a seamless wireless signal so that as I move throughout the house the routers will act as one router with multiple antennas? Is this a worthwhile effort or would extenders accomplish the same speed as something like this and will this work as I hope?

I would try to wire everything. I had a client who had a weak signal in an office which was a converted garage. The router was on the second floor, on the other side of the house. I ran a cat5 cable from the second floor, outside & around the house, to the first floor. I tucked in under the aluminum siding. The point is that anything can be wired & you're guaranteed a good signal.