Yes, in Add to Unlock (NEW) in the 'Gift With Purchase' reward, you have the option to select a checkbox 'Auto remove product(S) if the customer qualifies for a higher tier gift':
This checkbox is not automatically checked like 'auto add product to cart' and 'auto remove product(s) if the reward threshold is no longer met'.
So to prevent gifts from stacking, tick this checkbox.
You'll then see an additional text option for the reward information boxes titled: "Reward description after is removed from cart for higher tier gift"
The default copy for this is:
This gift has been removed from cart as a higher value gift has been unlocked
You can edit this description box to your own tone of voice/brand message.