Confused about strong/weak dibasic and tribasic acids?

I know that sulfuric acid is considered a strong acid, and the dissociation of its first H+ ion is complete and of its second H+ ion is partial.

Phosphoric acid is weak and all three of its H+ ions dissociate partially.

I just wanted to clarify- for dibasic and tribasic acids, are they considered strong if their first dissociation is complete (and subsequent ones will naturally be partial)?

I mean whenever you have a polyprotic acid/base and they say that if it is strong or weak you can only assume the first dissociation is strong or weak.

Say like you have $\ce{H2SO4}$ and we all know that it is a strong acid. This only means that the first dissociation is strong.

$$\ce{H2SO4 -> HSO4- + H3O+}$$

So in this case above only the first dissociation is strong. And then you cannot and do not know if $\ce{HSO4}$ is strong as well.

So overall in any case we cannot assume and the data must be provided. Good Question.

If you think about each dissociate state separately, than it's easy to answer your question. $\ce{H2SO4}$ is a very strong acid ($\text{pKa}\approx {-3.0}$), but $\ce{HSO4^{-}}$ is not so strong ($\text{pKa}\approx {2.0}$).

Phosphoric acid starts with $\text{pKa}\approx {2.14}$, which as as you said is not so strong, and $\ce{H2PO4^{-}}$ and $\ce{HPO4^{2-}}$ have $\text{pKa}\approx {7.2}$ and $\text{pKa}\approx {12.3}$, so definetly weak.

So yes, we say sulfuric acid is strong because we're talking about $\ce{H2SO4}$, and what comes after should be mentioned separately.