leaving room for more magic

Hard to say without knowing more about your plot... but my first inkling would be to have the knowledge lie within the elders of your ethnic groups - not to be used except for certain circumstances/events/prophecies/etc.

On the flip side, you could have younger characters find new magic on their own somehow. Through journeys, self reflection, books or cave drawings... the possibilities are really endless.

All that being said though of course, there is the disclaimer that you should only worry about one book at a time because you should never "pitch" a series.

Emerging magic could come from hidden sources (suppressed cults, lost knowledge), as a result of catastrophe in prior novels, hybridization or experimentation with existing magic, discovery of wondrous places or materials, or discovery of entirely unknown schools/types of magic.

You'd certainly want to seed these occurrences early on - scholars looking into things, travelers from afar, odd disturbances, etc.

Just have characters that don't use every type of magic available without explicitly forbidding other types of magic.

Liosse de Velishaf said:

Just have characters that don't use every type of magic available without explicitly forbidding other types of magic.

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That can become problematic from a consistency approach, i.e. if a character does something magical in book 3 for the first time, which could have resolved the conflict of book 1 300 pages earlier. Then you either need a good explanation why he didn't use it in book 1 already or try a different approach.
Personally, i'd just have different characters use different types of magic and not introduce all of them in the first book. Maybe different nations have different magic and book 1 only has mages from one nationality. Maybe different races have different magic. Maybe there's different schools/circles/styles/whatever of magic that are widespread but not so numerous that you run across all of them all the time. You could even pave the way for a later introduction by mentioning a few names of magic schools other than the ones featured in book 1, but without telling anything about their magic. Then they're not completely new when introduced in book 2 but you're still free to let them use whatever new magic system you think of.
Oh, and some general unsolicited advice: while it's very good to have a magic system to keep consistent with what mages can and can't do, it shouldn't actually feature (much) in the book. No-one wants to read about a character casting a third level spell. I've browsed some MMORPG books where that was the case (don't remember which MMORPG) and it made me cringe. If you've got the whole merchandising and advertising package of a million user MMORPG going for the book it might work, but i'll bet it's worth an instant rejection from an agent or publisher.

Lhun said:

Personally, i'd just have different characters use different types of magic and not introduce all of them in the first book.

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That's exactly what I said.

All my books take place on the same world, so I'm used to exploring different facets of magic in different books without contradicting myself. I just keep in mind the base rules of how magic works (which, for my system, is extremely simple).

Magic on the world I write about is really complex and convoluted with five completely different organized systems and a bunch of unorganized/random/individual powers, so that basically leaves it wide open for millions of variations. No-one can ever come close to fully understanding magic, and people are always coming up with new ways of using it. I hate it when magic systems are so organized and set in stone that they basically read like a computer game (which is no doubt what inspired them). If you go back to fantasy stories and fairy tales that pre-date computer and video games, you usually find magic portrayed as something mysterious, unpredictable, and poorly-understood.

ETA: I just noticed I said my magic system was simple and then in the next sentence said it was complex. What I mean is that its basic principals are simple. It's kind of like electricity. In and of itself, it's a very simple thing, but its uses are limited only by our innovation and imagination.

This is purely a matter of personal preference, not right & wrong, but I don't care for the idea; it sounds like two different stories unless the introduction of a "new" magic is the crux of the plot itself.

I would write an entirely new world setting and new characters if there's an entirely different way for magic to work. (Unless the multiple methods of magic were around and mentioned from the very beginning--one based on faith, the other based on academics, for instance.)

I believe the magic of a world should be deeply entwined in the story, the theme, the setting of this particular book. To jump to a whole new system suggests to me that you may need a whole new theme/story/setting to do it justice and fully explore it. But then, some folks love reading new magic systems as a sparkly tacked-on extra, just like a shiny new weapon, while I prefer to see magic as a device for exploring/enhancing conflict and theme in a story.

If magic is not the focus of your first, this should not be a problem.
Dont, however, shoot yourself in the foot by mentioning magic in the first book in any kind of detailed manner. Readers will expect you to be consistent.
If, for example, in the first, your MC is targeted by a curse, but in the next, you explain how curses simply cannot work according to the laws of magic blah blah blah, you have just ruined the reading experience for a loyal reader.
Another option, is to casually mention in the first one, that there are several systems/sources of magic in your world. Then you can create as many as you like later on.
In my own fantasy world, there are three. The science of Wizardry, spiritual Shamanism and dark Sorcery. Not one of my characters in my first novel know anything about magic, beyond the existence of the three. So for my next book, I could write about a Wizard, and for the third, write about a Sorcerer, without worrying about being inconsistent.

I was always a fan of the "Full Metal Alchemist" type of magic. It had a scientific sort of consistency to it, and yet was still something that in some ways was very mysterious.

I especially liked the idea of "equivalent exchange", as it sort of created a law of thermodynamics that governed magical systems. Nothing could be gotten for free, and everything had a price.

Dommo said:

I was always a fan of the "Full Metal Alchemist" type of magic. It had a scientific sort of consistency to it, and yet was still something that in some ways was very mysterious.

I especially liked the idea of "equivalent exchange", as it sort of created a law of thermodynamics that governed magical systems. Nothing could be gotten for free, and everything had a price.

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FMA used a dastardly and magificent trick, and one that may or may not be imitatable in textual mediums. They set only one major rule, which to be honest is the backbone of most magic, and painted a thin veneer of chemistry over it, with those lovely little circles adding a very nice visual counterpoint. Beyond the Law of Equivalent exchange and the use of some form of "circle", they said very little about the workings of th system. Then, they used good plotting and narration to avoid pissing off viewers/readers.

Dommo said:

I especially liked the idea of "equivalent exchange"... Nothing could be gotten for free, and everything had a price.

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They set only one major rule, which to be honest is the backbone of most magic.

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That was my first thought. The consensus of SF/F writers here on AW seems to be that "Nothing's free; there must be a price" is a prerequisite of magic. I've only heard disdain for magic that's "free" (and often for magic that's "cheap".)

Though maybe FMA is a testament to the power of colorful-yet-meaningless trappings, making a magic system look more mysterious or complex than it really is?

Ardent Kat said:

That was my first thought. The consensus of SF/F writers here on AW seems to be that "Nothing's free; there must be a price" is a prerequisite of magic. I've only heard disdain for magic that's "free" (and often for magic that's "cheap".)

Though maybe FMA is a testament to the power of colorful-yet-meaningless trappings, making a magic system look more mysterious or complex than it really is?

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I'd say it's a tribute to simplicity. They explain that one rule and then build an interesting and useful magical system and background out of it. I don't know how much of the system was worked out but kept behind the scenes, but whatever they did, it work narratively, which is what really matters in a story.

Yes, this is very common. Hell, even the Star Wars universe allows for it, with Force Witches, who summon and use the force differently than the jedi, and even other forces who have mystical powers not explainable by the protagonists, simply because it's outside their experience range.

You can see this not just in magic... but in tactics (like the Clan methods for attacking and fighting in the Inner Sphere when Kerensky's heirs finally returned to the Battletech universe), or in fighting styles -- the first time a kung fu fighter sees a style he's never heard of and is thwarted by it.

Things like these are game changers, though. They shift the universe on its side. You should know exactly how and why you're doing this, and then see how your characters survive. One way is to become better at the lore they have (Mhoram and the Lords of Revelstone had to do this once Foul and his Ravers possessed the illearth stone), another is to embrace the new magic and master it themselves.