Does adding mass to a liquid (not water) increase the volume
"The rule" is that an ideal mixture will have the volume of the sum of its components and the density will be the molar averaged density of the components. Real mixtures deviate from this rule to varying degrees.

The name of the property you're looking for that describes this deviation is "excess volume". Excess volume can be either positive (1L of A and 1L of B creates >2L of AB mixture) or negative (1L of C and 1L of D creates &lt;2L of CD mixture). The deviation from the rule depends mostly on how the molecules of the components interact with themselves compared to with the each other. Without knowing much about this specific case, I would guess that the big agar polymer molecules interrupt the local organization of the water molecules. This causes the density to decrease.

For many fluids, such as ethanol and water, the densities have been well studied and you can look up tables of excess volume. On a quick google search, it doesn't appear that anyone has ever done this for coconut water and agar. Unfortunately, that means more work for you. Fortunately, it means you get to break new scientific ground!