An acid with multiple protons does not need to be stronger than an acid with a single proton.
E.g. the acid H3PO4, which has three available protons, only is moderately strong. The acid HCl is much stronger.
For the acids, you simply have to remember how strong they are. Strength of an acid HA is quantified by means of constants Ka = [H+][A-]/[HA]. This constant tells how much of the acid is split into protons and the corresponding anion. There is much more to say about this, but for that I want to suggest you to read a good book on this subject.
When you have acids with more protons, then there are multiple Ka's for that acid. E.g. for H3PO4:
Ka1 = [H+][H2PO4-]/[H3PO4]
Ka2 = [H+][HPO4(2-)]/[H2PO4-]
Ka3 = [H+][PO4(3-)]/[HPO4(2-)]
For acids with multiple protons, the Ka for the free acid is larger than the Ka for the acid minus one proton and further Ka's are even lower. This effect is strongest, when the proton-delivering groups (frequently -OH groups) are on the same atom, as is the case for H3PO4 and H2SO4. When there are quite some atoms between the groups, such as in organic acids with long chains between the acid groups, e.g. HOOC-(CH2)8-COOH, then the Ka's for the two protons are almost the same, because of very weak coupling between the two ends of the chain.