Yes -
+5 - resistor - anode, cathode to TPIC6B595
Sure, can use two TPIC6B595.
One will control current into the anodes, one will sink current from the cathodes.
Connect the anode control between the resistor and the anode.
Connect 2nd TPIC6B595 between resistor & anode.
So, drive the anodes, letting them go hi/low as needed for a column with 8 outputs of one shift register.
WIth the other, pull the cathode low for that 1 column.
Anode current is then either going into the anodes, or into the anode shift register.