Q: Can Overload be applied to every spell?

A: No. You'll notice that cards with Overload use different syntax than those without Overload. Specifically, Overload spells always specify that it targets a creature you control or a creature you don't control. This way an Overload spell won't turn around on you when you want to use, for example, Mizzium Mortars, which would in all likelihood ruin your board state as well as that of your opponents. But even disregarding that, if you were to replace every single instance of "target" with "each" in every spell ever, the game would commit suicide. For just one example, Blood Feud. If you have any clue at all what "Each creature fights another each creature." means, you should tell Wizards.

Q: OK, that doesn't work. Is there any way to get a similar effect?
A: Yes. Here, I'll give you some wording taken from Glimmervoid Basin:

Whenever a player casts an instant or sorcery spell with a single target, he or she copies that spell for each other spell, permanent, card not on the battlefield, and/or player the spell could target. Each copy targets a different one of them.

This simulates Overload for cards with single targets well enough.