This option isn't set explicitly in the rules, but it can be added by introducing more mysterious forms of magic, like Artifacts, whose powers aren't initially clear. However, be careful to avoid making your players feel powerless by changing the consequences of their choices in the system without warning.
This isn't a question of "can spells do other things". Of course they can, even if there isn't anything explicit in the rules about this. This is a game of imagination set in a fantasy world, and spells can do as much or as little as you want, in addition to what it says in the rulebook. You could say, for instance, that Fireball and similar spells will slowly char the wizard's skin, or that necromantic spells could cause it to rot. All this is entirely within the realm of possibility for magic, especially in older editions, like the one you're playing, that haven't entirely entered the "rules are sacrosanct" mentality of 3e and newer editions.
However, what I would worry about here is players feeling cheated of their agency. The rules are there to give all the players a shared set of expectations, and unless properly introduced, telling them in retrospect "Oh, that spell you just cast? It also kills puppies" without any prior way of knowing is a recipe for frustrated players feeling that you're shifting the rug under their feet, and that's just plain Not Fun.
What you can do to mitigate that is to introduce this spell in such a way that its powers aren't clear and well defined, which can allow adding a side effect that isn't obvious. Don't just give the players a scroll with the spell, make a point of how mysterious and different it is. Have them find the scroll deep in a dungeon, written in an unfamiliar script, and after the wizard spends some time decyphering it, tell him he's reasonably certain of the spell's effects.
Of course, the pitfall here is to avoid making it too obvious that there's a catch to the spell. One way to avoid that is to have other spells - even most spells - be surrounded by this fog of confusion. Consider, for instance, the computer game nethack, where potions and scrolls are anonymous when first encountered, and you have to experiment to see what they do - in this case, you don't feel cheated if a scroll does more than you expected, because it wasn't too explicit in the first place.
A good place to look for example is books that detail unusual or powerful magic items, like AD&D 2e's Book of Artifacts. These are magic items that are described, a-priori as not obeying the standard rules. See this quote from p.6:
Artifacts are about wonder [..] so they have to be surprising, awe-inspiring, and unpredictable [..] Artifacts can't be ho-hum devices bound by the standard rules of magical devices — the dreary realities of charges, command words, and the like. Artifacts exist to break the rules.
A good analog for you here is the Book With No End (p.25), which is a spellbook with random spells inscribed on each page, and whose effects you can invoke - but at a cost. Since this isn't a normal spell-scroll or wand, but a book that is explicitly marked as different ("covers bound in the hide of a hatchling red dragon and hinged in gold. A golden clasp seals the volume and illuminated sigils emblazon the front and back."), the players will expect differences. And you can spring them immediately, or at your leisure.