Look at the structure for sulfate:
Why does sulfur form so many covalent bonds. Its valency is only $-2$, it only needs two electrons, yet here it's getting $6$.
The same thing happens with phosphate.
Phosphorus has a valency of $-3$, yet, it forms $5$ covalent bonds.
Answer
I think an important point to mention here is that Lewis dot structures, and the octet rule, are simply models that describe experimental observables. For example, the concept of valency works well with organic molecules but was challenged by Alfred Werner in the development of bonding models that adequately described coordination compounds.
The electron-dot model of bonding is so meaningful because it can be adapted to explain various experimental observables. You can draw two perfectly reasonable electron dot structures for $\ce{SO4^{2-}}$: one with all $\ce{S-O}$ single bonds and one with two $\ce{S=O}$ double bonds (and the additional resonance structures). The question is, which electron-dot structure best represents the real structure? We can use the concept of formal charges to predict that the structure with double bonds is most likely closer to reality.
We then look at the experimental data (which is reported on the sulfate wikipedia page) for S-O single and double bond lengths. The S-O bond length in $\ce{SO4^{2-}}$ is 149 pm, which is shorter than that observed in sulfuric acid (157 pm) and very close to the gas-phase bond length of sulfur monoxide which is 148 pm.
So, at the end of the day, an electron dot structure is a type of model that describes bonding. It has some additional features such as expanded octets and formal charge that help broaden its applicability to more situations; however, models such as this one don't tell us what an atom "needs"; rather, it provides an explanation for how we observe atoms "behaving".
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