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

Answer: 
> 
> Our last week's meeting 
> 
> 
> 

is a little akward, but I for one do **not** think that it is incorrect.

The answer by Tanner Swett says "it's never acceptable for a noun phrase to have more than one determiner." However, [the Wikipedia article](https://en.wikipedia.org/wiki/English_determiners#Combinations_of_determiners) lists eight different "common" cases where multiple determiners are acceptable. Specifically:

> 
> * A definite determiner can be followed by certain quantifiers (*the many problems, these three things, my very few faults*).
> * The words all and both can be followed by a definite determiner (*all the green apples, both the boys*), which can also be followed by a quantifier as above (*all the many outstanding issues*).
> * The word all can be followed by a cardinal number (*all three things*).
> * The word some can be followed by a cardinal number (*some eight packets*, meaning "approximately eight").
> * Words and phrases expressing fractions and multiples, such as *half, double, twice, three times*, etc. can be followed by a definite determiner: *half a minute, double the risk, twice my age, three times my salary, three-quarters the diameter*, etc.
> * The words such and exclamative-what can be followed by an indefinite article (as mentioned in the section above).
> * The word many can be used with the indefinite article and a singular noun (*many a night, many an awkward moment*).
> * The words each and every can be followed by a cardinal number or other expression of definite quantity (*each two seats, every five grams of flour*).
> 
> 
> 

...

> 
> As with other parts of speech, it is often possible to connect determiners of the same type with the conjunctions and and or: *his and her children, two or three beans*.
> 
> 
> 

The same answer says that "I drove this my car" is wrong. The form "this" followed by a possessive is now rare, but was once more common, especially in formal writing. In particular sentences such as:

> 
> It is a mistake to regard aspects of **this our present society** as unchangeable rules.
> 
> 
> 

were sufficiently common to be a style marker in the writings of the late Robert A Heinlein. 

Since the question title asks about using "two possessives in a row", this can certainly be proper. 

> 
> * This was John's father's watch.
> * This was King Mark's wife's cousin's castle.
> 
> 
> 

are both quite correct.
You can use two possessives in a row, that is not an issue. For example, if I have a cat, and my cat has a toy, I can say "my cat's toy." If there is a manufacturer for that toy, it would be somewhat acceptable, although convoluted, to say "my cat's toy's manufacturer," which would be three possessives in a row. If that manufacturer had subsidiaries, it would be much harder to follow, but you could probably still say "my cat's toy's manufacturer's subsidiaries." Though, with four possessives in a row, we'd probably rearrange the sentence structure to break them up some. 

In English, we would commonly say "last week's meeting," or perhaps "our meeting last week." We don't put an "our" modifier before a chronological modifier, such as "our last week's meeting," or "our today's meeting." The expectation is that "our" probably modifies the word that directly follows it, in other words, it sounds like "our" modifies "last week." But "last week," doesn't belong to us, so this sounds very weird. Unless you actually need the "our" modifier to clarify whose meeting *and* you need the "last week" modifier to clarify the time of the meeting, it makes sense to drop the modifier that is less helpful at conveying meeting.