One of the issues with this question is the rather ridiculous overmatch that firearms provide. Similar questions in Worldbuilding reveal that arrows shot by longbows can generate up to 100J of impact energy, and steel crossbows (drawn by some sort of spanning mechanism) can deliver 200J. An Arquebus from the 1400's can deliver 1000J of energy, an order of magnitude difference.
While humans have not become much stronger since the 1400's, firearms technology has advanced by leaps and bounds.
From the Atomic Rockets "Boom Table"(First column =energy in Joules):
Joules TNT equiv Ammunition
8.0 × 10^1 0.019 gram .22 short round
4.75 × 10^02 0.114 gram 9mm Luger Parabellum round
5.2 × 10^02 0.124 gram .38 Special round
5.4 × 10^02 0.129 gram .45 ACP round (Colt M1911)
9.4 × 10^02 0.225 gram .357 Magnum round
1.4 × 10^03 0.335 gram 3.5 g AK-74 bullet fired at 900 m/s
1.56 × 10^03 0.373 gram .44 Magnum round (AutoMag)
1.82 × 10^03 0.435 gram 5.56mm Remington NATO round
2.05 × 10^03 0.489 gram 7.62mm Soviet AK-47 round
2.56 × 10^03 0.612 gram .30-30 Winchester round
3.3 × 10^03 0.789 gram 9.33 g NATO rifle cartridge fired at 838 m/s
3.47 × 10^03 0.829 gram .303 Lee-Enfield round
3.74 × 10^03 0.895 gram .308 Winchester round (7.62x51 NATO round)
So except for the smallest handguns, the energy is going to be more than a human being can deliver in a hand held melee weapon, and it is being delivered in a smaller point and at a faster impulse time than a human can deliver the energy. To put it another way, you can certainly kill someone by shooting them in the head with a .22, but punching them in the head is far more likely to result in a set of broken knuckles for you.
So the short answer is that any effective armour against small arms is by default protection against virtually any muscle powered or hand held weapon as well. And since the people who make armour are not stupid, if there is a threat of things like stabbing weapons or icepicks being used against the target, they will weave or impregnate or add some sort of stab resistant layer. Even things like "Strike plates" over the most vulnerable part of the body can serve double duty, a metal or ceramic plate proof against the energy of a 7.62 X 51 NATO round can certainly stop a knife blade rather easily.
The only way to get around this is to look at real history. As armour became perfected towards the end of the 1400's ("Proof" armour is proof against gunshots, you can often see the dent in museum pieces where armours "proved" their product with a pistol or arquebus), and fluted or curved pieces deflected strikes by bladed or smashing weapons away from the user; long, narrow stabbing swords were developed to stab through the joints or gaps in armour.
Medieval Armor German Gothic Cuirass with Tasset
If this protection needs unarmored spaces at the joints to allow movement, or is "quilted" to prevent the fluid from leaking or draining to the bottom of the armour, then certain areas may exist where a very thin, extremely stiff, pointed blade might like an "Estoc" might work. (In the real world they evolved into rapiers and short swords)
Estoc. These are actually quite long and heavy
So except for particular situations (like an ambush), or living in a setting where carrying swords is acceptable civilian dress, people in armour are almost certainly going to be protected against both melee weapons and firearms.Modern police riot gear should be a positive demonstration of that.
Come at me bro
And Modern soldiers take this up to "11"