I will also echo garysk and Zaarin's kudos: head-marking and polysynthetic languages are things I feel we don't see enough of round here! I will also second all the advice they have given, which is very good.
Secondly, I would like to direct you to the seminal work on NI:
Mithun's The Evolution of Noun Incorporation. This will be very informative and explain a lot of the points. I'm going to partly rely on this paper for some of my explanation, so I would seriously recommend reading through it before looking at the rest of my post.
Thirdly, I'd like to point out that possessors in polysynthetic/head-marking languages are almost always expressed with some form of marking on the possessed noun. Indeed, the only polysynthetic language I've seen which doesn't do that doesn't have noun-incorporation either, which makes it even less relevant to what I'm about to say. Thus "For my cat" would be expressed 1s-BEN-cat (if you have cases, more on that below).
OK, now for the long explanation. Let's look at the example you give. I'm going to change the subject of "bought" from 1st to 2nd person, for reasons which I will outline below.
2s-buy-PST-3pl toys 1s-BEN-cat "you bought toys for my cat"
We incorporate the direct object (in this case "toys") like so.
2s-toy-buy-PST 1s-BEN-cat
If your language has type-2 noun-incorporation (again see the paper linked to above), which I presume it what you're getting at, then that noun's possessor/some other oblique argument would be promoted to direct object position like so.
2s-toy-buy-PST-3s 1s-cat
Note that the noun "cat" has lost its case marking; that it has "gone". To get what you've been getting at below, you'd do the same again, giving:
2s-cat-toy-buy-PST-1s "You cat-toy-bought me"
(If we were to go with your given example with a 1st person subject, then that'd be something like 1s-cat-toy-buy-PST-REFL with a reflexive, which would mess it up slightly).
As to whether incoporation of multiple nouns is attested, then yes, it is definitely attested.
when it comes to stranding, type-2 NI sorts this out by promoting some of the arguments. If you wanted to incorporate the noun "shoes" in "I bought red shoes", then you'd get something like "I shoe-bought those which are red". Note the relative-clause structure: in many polysynthetic languages, particularly in North America, adjectives are practically indistinguishable from verbs (I can't speak for those polysynthetic languages in Northern Australia where, like in the rest of Australia, adjectives are basically the same as nouns. they must do something similar, but I haven't got round to finding out what).
You mention applicatives. I see where you're coming from, and you can put them in if you want. You'd then get something like this.
2s-toy-buy-PST-BNAP 1s-cat
But the point with applicatives is to promote a prominent noun-phrase, so why you'd the want to then incorporated it I don't know. There must be languages out there which allow incorporation of applied objects, but I can't think of any. You'd probably end up with something like this.
2s-cat-toy-buy-PST-BNAP
If you were to allow this sort of thing, I'd probably reserve a special slot within your verb complex for oblique nouns.
On the other hand, this could be a valuable tool for allowing you to incorporate oblique nouns in a language which otherwise only incorporates direct objects.
If what you mean by the moving of case markers is the incorporation of
adpositions, then that is perfectly OK, and indeed is a very common occurrence in the history of the Na-Dené languages.
Now you don't need case markers or adpositions at all, really. There are quite a few languages out there which use verbs or nouns for the same purpose. These could possibly be stranded when the oblique noun is incorporated as well. An interesting possibility would be to permit verbal compounding as well (like serial verbs only in one verb). So "You bought toys for my cat" might be expressed thus:
2s-buy-give-PST toys 1s-cat
This is when unincorporated. Then when you incorporate the nouns you could have then before their respective verbs, like so:
2s-toy-buy-cat-give-PST-2s
(I am of course presuming you have a single, morphologically indivisible word for toy, which I doubt would be the case in a polysynthetic languege; you'd probably have a nominalised clause à la "that which is played with".)
Finally, if I was doing a polysynthetic language, I'd be tempted to express "you are filled with determination" with "determination fills you", which rather prevents incorporation (if you're going for naturalism at any rate".