This seems like an important question, but different searches using different phrasings returned no matches. I apologize if it has been answered before. Here is my question.

When applying enchantments from books to items, I’ve noticed that often no level improvement is shown. For example, applying a sharpness level II to a sword with sharpness III will show no change, even though the player is charged full price in experience for the ‘upgrade’. In the most extreme example, I have a crossbow with level IV piercing and a book with level IV piercing. Placing both items on the anvil shows a cost of 35 experience, but the resulting crossbow shows as the same level IV. Would using this rare and precious book on the crossbow be wasted, or am I better off waiting until I can combine two level IV piercing books to obtain a level V, and then apply that to the crossbow? In other words, would applying the level IV piercing to the crossbow increase the float value of the enchantment (even though it falls short of the level V displayed integer) and so carry over until I can apply additional piercing enchants (say several level II’s or a level III) to reach the next full displayed integer level V, or are integer values only used, and anything that fails to reach the level V integer is wasted and lost, at the expense of exp?