Range Extenders

Yes, any number of WiFi extenders can be connected to a WiFi router.  Typically, the extender should be close enough to the router to get a good signal and also close enough to the device being connected to provide a good signal.  Often "half way" is a good compromise, depending on the building construction.

An important consideration is how the target device expects to connect.

• If the goal is to provide an Ethernet connection, then obviously the WiFi extender needs to be in the same room as the device.
• If the goal is to "extend" the WiFi coverage, then I would start with about "half way" and see how it goes.

People often have a choice of having the WiFi extender broadcast the same WiFi credentials as the primary router or defining a different WiFi network name.  This is often useful in preventing the target device from attempting to connect to the primary router rather than the extender.