Can two precipitates form in a precipitation reaction that starts with only two compounds in water?
The number of examples is considerably great.
Consider the following:

$$\ce{Ba(OH)2(aq) + MgSO4(aq)  -&gt; BaSO4(s) + Mg(OH)2(s)} $$

Above reactants are reasonably soluble in water.
From Wikipedia, $\ce{Ba(OH)2} $ has a solubility of 1.67 g / 100 mL at 20 °C and $\ce{MgSO4} $ a solubility of 25.5 g / 100 mL at 20 °C