How to make water render around an object instead of all in front or all behind?

I’m having a similar problem to this one I had before, where my objects are not rendering in the right order: Render order is not correct for mesh renderers?

I have a plane of water, which is a semitransparent material, and a dog sprite, which is an alpha cutoff material. I would like the dog to be able to appear partially above-water and partially underwater when it’s in water. However, it only renders either completely in front of the water, or completely behind the water. I can’t use the solution from the question above, because this time, one of the objects is semitransparent. Is there a way to fix this?