A quick video showing the current method for wearing both clothes and armor.

You’ll need to obtain a special undersuit that will allow you to use this.

You’ll need to set the primary action on the action wheel to “Equip” (middle mouse button sets the primary action) for undersuits.

Then have the undersuit next to a large cargo box with some clothes in it and equip the clothes as your character is performing the animation to pick up and equip the undersuit.

Edit: typo