If I had known you would be late, I would've waited for you.

I think this is correct.

Can I say without changing the meaning,

If I had known you were late, I would've waited for you.

I think the fact that you were late is what the speaker already know right now, so the past simple could be used in the if-clause. It could be casual spoken English, though.

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Comments  (Page 3) 
Oh my, I'm so surprised! I would never have thought you said it yourself! By the way, you said "If I'd have known", and not "If I'd known" (which can't mean "If I would have known", because you would be leaving out a syllable...).
Anyway, I'll tell you the truth: I've always thought it was non-standard, same register as "ain't". Low register, only common in certain dialects. I don't remember a single grammar book saying it was acceptable. In fact, I only remember people criticizing it. Here are a few comments like the ones I've always heard:

Also in the midwest, I often heard, "If I would have . . . ., I would have . . . . ." Drove me nutz! (Avangi)


The construction, actually any construction with 'would' in a hypothetical if-clause, is considered non-standard. (Jim)

To me, it evokes comical people from remote mountain regions or from city slums who are uneducated and have some accent that most listeners dislike. But maybe research would reveal it to enjoy a wider demographic distribution. To my ear, it's about as obtrusively wrong and amusing as 'them' for 'those'. It's definitely not acceptable for standard written usage. On the other hand, it's not the most awful mistake one can make. (Native from San Diego)

Would have for had -
In spoken English, there is a growing tendency to use would have in place of the subjunctive had in contrary-to-fact clauses, such as If she would have (instead of if she had) only listened to me, this would never have happened. But this usage is still widely considered an error in writing. Only 14 percent of the Usage Panel accepts it in the previously cited sentence, and a similar amount—but 16 percent—accepts it in the sentence I wish you would have told me about this sooner. (A Practical and Authoritative Guide to Contemporary English)

On the other hand, some people seem to use it all the time, regardless of region or cultural influences, and so it's a common feature of informal English to them. One example:

Hmmm...never thought of that construction as a mountain dialect but normal everyday American! I never knew it was incorrect! (Native from the Midwest)

That's why I was so surprised, considering you are a writer and knowing you use "correct" English most of the time. This can only mean two things now... I have to choose between:
1) I start to use it as well, feeling ashamed of not knowing is was so common.
2) I don't start to use it, and I start to tease you because it's not like you to speak bad English. Emotion: big smile

LOL, just kidding. Seriously, I don't know what to say. I think I'll consider the fact that people are actually more tolerant of it than I thought, so it's not that bad. But do you also use it in your writing? You know, just because I don't like prescriptive grammar, doesn't mean I don't want to know about it. In fact, prescriptive grammar is part of descriptive grammar. Emotion: wink
I'll appreciate any opinions on this. Thanks.
Gracious God in Heaven! If I'd have known this would have become such a huge topic...

Yes, I would say this and write this. I guess I have to move to the Ozarks now.
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Wow, cool. I would never have thought it was ok in writing... Thanks.Emotion: smile
In BrE, on the other hand, the "if X'd have done Y" construction tends to represent "if X had have done Y", not "if X would have done Y", and has the same meaning as "if X had done Y". It also turns up in an inverted form, e.g. "Had X have done Y" (or "had X a done..."). It tends not to appear in published texts, except in dialogue (cf. the example in The Great Gatsby – "If we'd of raised the blinds, we'd of seen daylight", where "of" = "have").

"If X would have done Y" is also moderately common in spoken BrE, especially in northern dialects, but seems to have a sense of "if X had been willing to do Y". Again, you tend not to find it in published texts.

(I note that MS Word objects to "If I'd've", but not "If I had have". Curious.)