You can have 2 routers in a LAN segment but, unless they are extenders, they need different IP addresses.
What I have now is this.
Cable modem - Gigabit Ethernet Switch - to 8 things.
1. 4 port router with DHCP enabled but no WiFi (static IP address on LAN)
2. Ethernet printer
3. Desktop PC
4. Ethernet run to a room to a central place in the house
5. Gigabit Ethernet switch #2 in home entertainment center in living room
6-8 open
4 is a run to a router set up as a WiFi Access Point. DHCP disabled. It points to Router #1 for it's addressing. Static IP address on LAN.
Router #1 gets WAN addressing and connectivity from ISP.
Router #2 gets it's LAN info from Router #1.
Hardwired items get info for LAN from Router #1 (and bypasses the router for PtP traffic inside the LAN because of the switching, so the router only loads up for LAN/WAN routing and DHCP management).
WiFi items get info from Router #2 which then passes LAN traffic through the switch(es) or through Router #1 for WAN traffic.
You can have overlapping WiFi zones on the same LAN segment with range extenders or by setting up each WiFi with a different LAN IP address (last octet) and different SSID. If you're mobile while connecting and moving between zones, you could lose/acquire connectivity while moving between zones (handoff) but the devices' ability to reacquire connections will be dependent on the device and if you have auto-connect enabled to known networks. The disadvantage of this is the gap in connectivity while moving between zones. The advantage is that standard, low-cost WiFi routers can be used. For better, since SSID/IP/WiFi connections, range extenders would be the way to go in spite of their (usual) higher cost and lack of flexibility for use in other configurations (backups for main router, etc.).
There are some VERY neat solutions that include POE (power over Ethernet) and multi-zone WiFi coverage.
http://geekbeat.tv/unifi-wireless-system-review/http://geekbeat.tv/editors-choice-open-mesh-wifi-network-for-large-homes-and-small-businesses/