If the suspended particles are insoluble in the liquid, then you will simply have another suspension.
A miscible liquid is one in which two or more liquids are mutually soluble. They mix homogeneously to form essentially a single liquid.
A suspension is the continuing movement or entrapment of fine solids in a liquid. They do not usually or easily precipitate out of the solution.
So, mixing a suspension with another miscible liquid just depends on whether the suspension liquid is miscible with the other liquid, and whether the particle is soluble in the miscible liquid or not. If it is not, then you will have another suspension. If it is soluble, it will cease being a particulate suspension and become a solute in the solution.