An ionic compound dissociates into 3 ions of 3 different elements? When an ionic compound dissolves in water and becomes ions. 

1) Typically we see:

$\ce{AB -&gt;}$ Ions $\ce{A+ + B-}$

$\ce{ABC -&gt;}$ Ions $\ce{AB+ + C-}$

2) But how about the one below, is there any case that will fit the situation

$\ce{ABC2 -&gt; A+ + B+ + 2C-}$

or $\ce{AB2C-&gt; A+ + 2B+ + C^3-}$
Yup, they are definitely possible. Such salts are called as mixed salts. They furnish more than two ions when dissolved in water. A popular example is Mohr's salt, popularly used as a standard titrant to measure concentrations of oxidizing agents. It's (anhydrous) formula is:

$$\ce{Fe^{II}(NH4)2(SO4)2}$$

This salt on dissolving in water would split as:

$$\ce{Fe^{II}(NH4)2(SO4)2 &lt;=&gt;&gt; Fe^2+ + 2NH4+ + 2SO4^2-}$$

This is one such example. There are many others, notably alums. Alums are a general type of mixed salts, of the form:

$$\ce{A^{I}M^{III}(SO4)2}$$

where $\ce{A^{I}}$ is a monovalent metal ion, and $\ce{M^{III}}$ is a trivalent metal ion. Clearly, these are also mixed salts.

These are just a few practical examples. There's literally quite nothing that can stop imagination of course.