Question: Following a previous discussion about **I would like** vs **I would have liked**, I have a similar question.

What is the difference between

> 
> I wanted to come to your party but I couldn't 
> 
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> I would have liked to come to your party but I couldn't.
> 
> 
>

Answer: 
This sounds like one of those rules that someone made up because they could think of examples where breaking it caused problems, but didn't try to think through if breaking it would ALWAYS cause problems.

Well, off the top let me point out that the rule as worded, "never use two possessives in a row", is clearly wrong. People do that all the time and it makes perfect sense. "My dog's bone", "Fred's car's engine", etc. In examples like that, the first possessive modifies the first noun, and then that phrase is used as a possessive to modify the second noun. I mean, in "my dog's bone", I am saying that the dog belongs to me, and that the bone belongs to this dog which belongs to me. Both possessives are not modifying the same word. It is not "my bone" and also some "dog's bone".

But I assume that whoever made up this rule meant that you cannot have two possessives modifying the same noun. You can't say "Fred's Bob's car". That example clearly doesn't make sense. Is it Fred's car, or is it Bob's car? If it belongs to both, you need to join them with an "and", like "Fred's and Bob's car". If you're not sure of the ownership, you need to join them with an "or", like, "The red Chevy is either Fred's or Bob's car".

But possessives are used for many things other than ownership. If I am at work and I refer to "my desk", I probably don't mean that I own the desk, but rather that this is the desk where the company has assigned me to sit while I work. If I say, "my state", I don't mean that I personally own the entire state and everything in it. I simply mean that I live there. Etc.

So if I say "our meeting", I don't mean that I own the meeting. I don't know what that would even mean. I mean the meeting between you and me, or possibly the meeting that you and I organized. If I say "last week's meeting", I mean the meeting that happened last week. There is no reason why a meeting could not be both "our meeting" and "last week's meeting", so "our last week's meeting" is a perfectly sensible thing to say. And indeed people say things like that all the time.

Yes, USUALLY two possessives in a row that both apply to the same noun is wrong. But it's not valid to say that because something is USUALLY wrong that therefore you should NEVER do it.
"Our today's meeting" means literally "(the) meeting of our today". This is why it's wrong. I believe we all agree that nobody would say "meeting of our today".