There are a lot of spells in D&D, with a lot of them requiring spell slots or just part catrips. But what if there was a way to combine spells or create different variants of them? I'll use magic missile and fireball as an example. What if you could find a way to combine magic missile and fireball to make magic inferno missile, which could have less damage but an added effect of giving fire damage to all enemies in a 5 meter radius. Maybe turn fireball into fire barrage? That could have maybe a fraction of the original's strength but can be shot in a 3 burst round, hitting multiple enemies at once. This is just a rough idea that could be refined in a home-brew of sorts, I just wanted to have the opinions of experienced players and see if this was an idea worth committing to. So please tell me what you think?

Sounds like a cool idea thought this is from a player who more on a creative side of things then years of playing D&D
Anyway there should be a degree of success & failure for the characters on making a new fused spell. if the two spells are from the same level (like two 1st lvl spell), the higher the chance of a new spell is created that can be discussed between you and your DM on how this new spell works, but then if you try to fuse a spell that from two different levels then the degree of success shifts. 

Also it hinged on who is making the new spell. Wizards, Warlocks and Sorcerers might have a better chance if they have a high INT/CHA modifier or high Arcana skill while other classes might struggle unless again if they have a high required INT/CHA or Arcana skill but this is my view on your cool idea.

There are some basic guidelines in place to help you out if you want or you can just go wild and make what you like. Here is the section in the DMG:

https://www.dndbeyond.com/sources/dmg/dungeon-masters-workshop#CreatingaSpell