Change Color1 on your mix node to the color of your character.

Select Multiply instead of Mix in your Mix node.

Disconnect your Alpha from the Image Texture node.

Change Color1 on your mix node to the color of your character.

Select Multiply or Overlay instead of Mix in your Mix node.

Disconnect your Alpha from the Image Texture node.

You may need to reverse your Color1 and Color2 in your mix node depending on which option you choose.