I have a Lenovo laptop with a single USB 3.0 port.
I am using a four port USB 3.0 port extender.
Can I plug in another extender into one of the open ports and will it work.
If your "port extender" (read: "USB 3.0 hub") does not have any external AC-DC power adapter, you can use only one downstream port with full theoretical capacity. Actually, it should be less than one port, since the entire power comes from a single laptop port, and some of this power must be wasted to power the internal hub chip controller (which can be about 1 W, or about 200 mA from the 900 mA official USB 3.0 port budget). If you use another non-self-powered "extender" (with no AC-DC adapter), similar consideration would apply to it: you can use only devices with power requirements under 500 mA total (another 200 mA will be needed for powering internal IC in the second "extender").
However, if your "extenders" do have proper external power supplies, there should be no restrictions whatsoever, it should work with every USB 3.0 or 2.0 devices, including bus-powered HDD enclosures. Proper power supply for a 4-port hub must have at least 4 A capacity at 5 V.
Of course, the laptop port might be able to supply more than the official 900mA, but you should not be surprised that some ("high-powered") devices will behave erratically.