Hammers and daggers became increasingly popular as full plate armor entered the battlefield. Even a full suit of armor must have gaps, if the person inside is to move. This opens up space for a dagger or the point of sword to slip in and strike the opponent. Fiore de Liberi's Flower of Battle, for example, has an entire section dedicated to grappling with opponent so that after forcing the other person into a hold, a dagger can then be pulled out and thrust between their armor. Dedicated warhammers gained in popularity in tandem with plate armor; even though a blow would never actually penetrate the armor, the sheer force would crush bone, dent plate and give a seriously nasty contusion.

In addition to the comments already made, note that much of the armour on a late Medieval plate armour is thin enough so that it can be penetrated by crossbows or arrows. Usually, the breastplate and helmet are thick enough so that they can be considered arrow-proof (often 2-3mm thick), but arm and leg armour is usually thinner (often 1-1.2mm, or even thinner), and can be penetrated. Arms and legs aren't particularly vulnerable, since the armour is strongly curved, and a crossbow bolt or arrow is unlikely to hit square-on.

Arms and legs will be more vulnerable to polearms, maces, etc. in hand-to-hand fighting.

Finally, note that handheld firearms were already being used in Europe in the late 14th century. Depending on what you call "full plate armour", this can mean that the gun preceded full plate armour, so your question as-asked might not be answerable historically (practically, yes). But also note that 3mm thick armour provides reasonable protection against early (e.g., 15th century) handheld firearms (See Alan Williams, The Knight and the Blast Furnace for the penetration of armour by crossbow bolts, arrows, and bullets, and some thickness measurements.)