The AirPort Time Capsule can be set up as an additional access point to extend the signal from another non-Apple router......IF......the Time Capsule is connected back to the main router using a permanent wired Ethernet cable connection.
If you cannot run the Ethernet cable, then it might be possible to use a pair of Ethernet over Powerline adapters to send the Ethernet signal from the main router to the Time Capsule over the existing AC wiring in your home.
I am not recommending that you use these types of devices, only mentioning them as a possibility if it is not feasible to run and install the Ethernet cabling......which would be the best option by far in terms of performance.
In other words, the theory with powerline adapters is that you already have the wiring in place.....you just need the adapters. In practice, things do not always work as well as the theory suggests, so if you are considering the purchase of powerline adapters, it would be a good idea to understand the store's return policy in advance.....before you buy.
As far as having the AirPort Time Capsule function as the main router......this will depend on the type of modem that you have. The Time Capsule requires a simple modem......(it will have only one Ethernet port)......to function as the main router on the network.
If the device that you call your "modem" is really a modem/router or gateway device........(it will have multiple Ethernet ports and provide WiFi service)......then the Time Capsule cannot be the main router for the network with this type of device.......unless......your modem/router or gateway can be modified to act like a simple modem. Check with your Internet service provider to see if this might be possible with your existing device.