Can/should a novel contain multiple premises?

Let me qualify this question before you answer it.

I've been reading How to Write a Damn Good Novel by James N. Frey, going along the book like it's a mental check list to see if I've been a good boy with my manuscript.

I'm 64 pages in, thinking "So far, so good." I obviously did enough reading before I tried writing to intuitively pick up on the expectations of readers such that my manuscript violates no major rules. I didn't even start my third draft (noticeably better according to my alpha readers) until I finished a conscious introduction to literary theory. I'm not just a wide-eyed wannabe, I think. I've got real potential!

Until I read the sentence "A novel contains one, and only one, premise" and I agreed. Sort of. (Worth noting that many of these lessons have been put forward by considerably older theorists--Frey does not claim originality to these theories, he has simply compiled them in one easy-to-read place and provided examples of their application).

Now, Mr. Frey/Aristotle had previously stated in the same work that "A dramatic story contains one, and only one, premise." He used the word story, book, and novel almost interchangably--which, to be fair, so did I.

The next point that was made was that every scene, every line of dialogue and every word you put in your manuscript must take steps to prove that premise. Once again, I wholeheartedly agreed. I think this is what pros call "trimming the fat."

So I was giddy with joy when I looked at my manuscript and identified a premise right away. Then my face fell, when I realised a secondary aspect had its own premise, independent of the first. Then I started crying, because a tertiary aspect had yet another premise. My novel has three separate premises.

So, my question to you fine people at Absolute Write, as as follows:

Can a novel contain multiple stories, and still be a unified whole? Would each of those stories prove their own premise without intruding on one another?

I am not reluctant to "cut the fat" from my manuscript (my first and second drafts have contributed exactly one sentence to my third). That said, the secondary storyline in my manuscript (a romantic sub-plot) exists to garner sympathy for the MC and her partner--so that when they're put in danger by the main plot later on, the reader has greater interest in seeing the characters succeed. Without this sub-plot, I've had less opportunity to show what makes my MC different from MCs of the genre. Now that I understand that a "good" book is simply one that contains carefully planned pages where each and every scene contributes to the premise, I'm worried that I'm threatening my main premise by making it proximal to an entirely unrelated one.

For those interested, I'll give my premises:

In the main plot, a murder mystery, the premise proved is "persistence will result in answers."

In the romantic sub-plot, the premise proved is "open communication leads to stability."

In the tertiary, "day job" case, the premise proved is "not all suspicious people are guilty."

Perhaps this will help you understand my concern--these three premises do not contradict one another, and are only linked by the character. Each could be a story unto itself, but each also serves their own "meta" purpose like giving credence to the MCs credentials (she's the daughter of a private eye) or again, garnering sympathy so you actually give a damn when I threaten the lives of the characters.

Am I shooting myself in the foot or just misinterpreting Frey/Aristotle's meaning?

From How to Write a Damn Good Novel:

Every good premise should contain an element of character which through conflict leads to a conclusion.

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From The Writer's Compass (Nancy Ellen Dodd):

A theme is what you are trying to say, a premise is what you believe to be true or false and want to prove.

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So, not to be inflammatory--but for the sake of not getting caught up in semantics I speak of Frey's and Dodd's definitions when I talk of a "premise" being "a statement that can be verified as true or false with the context of a story."

Any other experiences from my fellow writers?

Thank you all for your lovely responses

And yes, I do get caught up in definitions. You can't argue on whether something is X unless you know what X is, which is my beef with a lot of philosophical traditions!

SomethingOrOther - your math analogy is surprisingly apt!

Luckily my hiatus off the forum was spent doing exactly what everyone is telling me to--writing, and not worrying. Still, I wanted to see what others had thought on the subject.

writing is writing and music is music, but a symphony contains several themes, melody lines, orchestral colorings and, like a novel, the good ones all work together to create a cohesive piece.

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If I had a medal to give you, it would be for this.