solubility in parts

so i was out at the newbury st tea-luxe drinking some masala chai w/rachel and i had an interesting question that neither of us really new the answer to. i had a lot of high school chemistry theories but nothing really substantial.

while drinking tea, you end up disolving molecules (like sugar) into the water. at a certain point the water could become saturated, at which point additional sugar stays in a solid form. the tipping point at which this happens (iirc) can be observed through titration protocols, or possibly calculated using some stoichiometry equation. there was a point at which we ran out of one type of sugar and rachel switched to another, making the comment "this could be different/better sugar anyways."

it got me wondering, is solubility of multiple types of solids in the same body of water associative? or in other words:

can you compute solubility of water + sugar0 + sugar1
as simply as
(water0 + sugar0) + (water1 + sugar1) ?

i'm wondering if there are other factors involved in this equation, like maybe:

• the order/amount that you add each solute
• any characteristics or interactions ocurring between solutes
• of course there are things like temp, pressure. pH?
• any others?