Is there any solute-solvent interaction possible, in such a way that a solvent with mass X grams and volume Y litres, and a solute with mass A grams and volume B litres, to form a solution that has exactly the same mass and volume as that of the solvent (X grams and Y litres)?
As Klaus suggests above, you can't add mass to another mass without it increasing. That would defy the first law of thermodynamics that energy cannot be destroyed since mass and energy are directly linked.
However, much of this depends on what degree of precision you're measuring to. If you're working with a cubic metre of water and only measuring to the first two significant figures, mass would be 1000kg and volume 1000l, and you add 40kg of sodium chloride to make a 4% saline solution, you would still only have 1000kg and 1000l because you're not counting the third significant figure.
It's all about context ;-)