Yes you can, if your card support it. First of all look the documentation of iw and especially the page of virtual interfaces. Unless you are running 14.04, that is, due to a bug in udev scripts (probably fixed in 15.10, but no confirmation yet).
Note that in the following description
wlan0 is my normal WiFi interface and
wlan1 is the name I choosed for the virtual one (it's quite arbitrary). You have to adapt this to your system, of course.
You can create a new virtual interface with:
sudo iw dev wlan0 interface add wlan1 type station
if your adaptor/driver support it, it's done --- you now have two interfaces; otherwise you will have some type of error or the interface will not appear.
You can check if the new interface exists by typing
sudo ifconfig -a
...and see if the
wlan1 interface shows up. It will appear in the Network Manager too anyway:
You can remove the virtual interface with
sudo iw dev wlan1 del
I really never used it --- I tried to connect twice to my router and havoc arose (but that probably is normal). Moreover, you will probably need to see if packet forwarding between the two interfaces is enabled by default or not, and you probably need to play a bit with the routing after that. But it's a start.
PD --- one of the thing you will probably have to change is the MAC number of the "virtual" interface, which is by default the same as the other, and will create problems almost for sure.