Is it possible for monobasic and dibasic potassium phosphate to complete break down into phosphates?
At basic conditions over pH 10, those phosphorus-containing anions can get further deprotonated, as can easily be seen on the corresponding Wikipedia article on phosphates.

Phosphoric acid $\rightarrow$ Dihydrogen phosphate $\rightarrow$ Hydrogen phosphate $\rightarrow$ Phosphate