Is it possible to run two vlans on same switch port?

Yes it is possible to run two vlans on the same port. There are Multi Vlan Access port (MVAP) which are consist of two vlans,

-Data vlan (PVID)

-Voice vlan (VVID)

This allows the user to seprate Voice traffic and Data traffic  to different VLANs.Usually the dynamic ports can belong to only one VLAN at a time.

The MVAP (Multi Access Vlan Access port) on Cisco switches require the second VLAN to be voice VLAN advertised by CDP and in the absence of CDP, it does not work. Thus, you cannot use MVAP as a data VLAN. Its only use is for voice.

e.g. If you have a data VLAN and a voice VLAN, your IP phone at your desk connects to your PC on the same port, however they both need to have access to two different VLANs.