Two ampoules of potassium dihydrogen phosphate will give you 20mmol of potassium and 20mmol of phosphate.
In this scenario, let us use KH2PO4; however sodium dihydrogen phosphate is also available.
The potassium does its intracellular thing, distributing according to the magnitude of total potassium stores, as described previously. In summary, starting with a potassium of 3.5mmol/L and with 10% remaining extracellular, the serum potassium would rise by 0.14mmol/L, up to 3.54mmol/L.
Of the 20mmol of phosphate, some proportion remains extracellular and some proportion is transported into the cells. The magnitude of each proportion is reliant on numerous factors, which makes it difficult to come up with a theoretical model of potassium distribution which one might use at the bedside.
Thankfully, somebody has infused some phosphate into people, and taken careful measurements.
French and Bellomo reported on the effects of infusing 14.5 mmol of KH2PO4 into critically ill patients. With this dose, the phosphate increased by a mean figure of 0.65mmol/L. If we assume that the extracellular fluid volume in these patients measured a precise 14 litres, we can estimate that 9.1mmol (65%) of the infused phosphate remained extracellular.
If my model were to replicate this result, 13mmol of phosphate would remain extracellular, with the serum phosphate increasing from 1.0mmol/L to 1.93mmol/L.
Water will slosh around the compartments, but not to an extent which would provoke either baroreceptors or osmoreceptors to react. The serum osmolality rises by only 0.8mOsm/L, and I don't want to get into the changes in volume, except to say that they are miniscule.