Yes: your game, your rules, your weapons table
I’d like to provide a different take from the other answers, which I feel ignore a crucial rule of the game.
This is Dungeons & Dragons, which, as a TTRPG, puts the power of game content and rules squarely in the hands of the DM. The game is based on one core mechanic (quotes later when I have my books):
- The DM describes the situation
- The players describe their characters’ actions
- The DM decides the results.
Being essentially the introduction to the game, this mechanic should be at the heart of gameplay. It is precisely this mechanic that affords D&D (among others) the extensive creative freedom not found in books or even some video game RPGs. There is a human (you) running the game, not a computer.
All of this to say, it is perfectly within the rules to create your own weapons table with unique properties, modify the original, or anything else you see fit. But you might want to consider a few things:
- Why? What purpose will this serve? How will it enhance my game or detract from it?
- How? How can I do this in a reasonable way? How (and when) will I communicate this to the players?
- What if...? ...it goes horribly wrong? How does the table handle it?
For example, with weapons, this is something that needs to be communicated concisely and up-front, since it affects most characters most of the game. I’m usually ok with reverting rules changes to the standard version when I screw up, but YMMV. And honestly, a single tweak here or there may not enhance the game much overall (but if it lets one player build their dream character, perhaps it’s worth it? Perhaps reskin something instead...).
You may also want to consider the balance of the game, something impossible to consider here without specifics, but note that balance is highly table dependent and can be tweaked to achieve certain effects (standard AngryGM language warnings apply).
Finally, I direct you to this AngryGM series on new armor tables as inspiration for your modified weapons. Part 1 Part 2
NB: there are no mechanics presented in the core rules foe this kind of tweaking. But there certainly is a rule that allows it (the table in the PHB is unchangeable, but what you use in your game is not “fixed”).