I was learning about adjectives + さ, which turns them into a noun; as I understand it, a "measurable" quantity . I then thought of how X そうです could be turned into an adjective, X そうな Y, so I was wondering whether if さ could also be applied here. If so, is this something actively used in the language? If not, what sort of limitations does さ have in general that prevents such an usage?
I don't think this is a very good question but rather than ignore it, I will try to explain why in an answer.
First let's confirm what you are asking:
Grammatically "i-adjectives" and "na-adjectives" can combine with そう to form new na-adjectives which decribe how a situation seems (as opposed to actually is). Examples include:
おいしい ー＞ おいしそう（な）｜delicious -> looks delicious
元気（な）ー＞ 元気そう（な）| healthy -> seems healthy
These adjectives can also combine with さ in a similar fashion:
おいしい ー＞ おいしさ｜delicious-ness (how delicious it is)
元気（な）ー＞ 元気さ | healthiness
You have noticed that the -そう combinations are all "na-adjectives" and grammatically could be combined with さ to form some kind of noun and want to know if this happens.
Well, grammatically, we just demonstrated it is possible, and somebody has even found a tweet with such a combination. But, it is the first time I have seen such a construction used. It is certainly not something I have noticed before or been taught, although, like you, I might have played around with the combination in my own mind.
But, more importantly, what "words" did you have in mind and how did you foresee this construction being used? If you considered this and showed it in your question then it would have been more valid.
Conceptually it might be easier to look at the English equivalents: "looks delicious" is fine. "How nice it is" is better than "delicious-ness" but the latter is still understandable, and an equivalent might exist in another language. But, can you really go to the next stage and come up with a similar word in English ("looks-delicious-ness") that you would expect to find in Japanese? We could say "how delicious it looks", but this is a phrase and by itself sounds more like an assertion. You might conclude that the concept has to be expressed differently (in both languages).
Japanese is very different from English so sometimes one does get a surprising answer - somebody might read this and tell me that I am completely wrong and although I have not noticed it, ~そうさ(な）is a valid construction often used.. but I am not expecting that to happen.
It also important to focus on developing a practical feel for how the language works. If you have got to the level of studying these constructions then I would have thought you have a sense of how they are used and how many theoretical combinations and conjugations are possible. So, just like English, once things get unwieldy, there is probably a better, simpler way of saying it.
Let's take another example:
高そうさ｜"looks expensive-ness" (it does not really work in English either)
Now if we really want to ask someone how expensive does something look, what would we say?:
The second sounds more natural to me, although I have never heard it said, and there may well be a better way of saying it.
I think one needs to distinguish two uses of ～そう. The one appears after a stem form, and is a derivational suffix of the na-adjectival class (NA). The other one appears after a fully inflected expression, and is thus particle (P). Here are two examples:
a. その店、おいしそうだ。(NA) That shop looks tasty. (i.e. the food they sell there) b. その店、おいしいそうだ。(P) That shop's supposed to be tasty.
In (a) the assumption for tastiness is derived from personal knowledge, in particular from looking at something. Technically, this is called "evidentiality". In (b) the knowledge is derived from hearsay, i.e. we've heard from someone that something is to be the case.
Only the ～そう in (a) can appear with ～な:
c. おいしそうな店だ。(NA) a shop with tasty looking food d.* おいしいそうな店だ。(P) a shop I heard is tasty
Expression (d) is not possible, which is what the appearance of the asterisk * tells us.
Concerning the combination of these two expressions with ～さ, this happens only in two cases. The adjective 良い（いい・よい） only has one mora in the stem. ～さ appears between ～そう（な）and 良い. See here:
e. それは良さそうだ。 That seems good. f. 良さそうなもの something that seems good
There is one other adjective, namely 無い（ない）, that also has only one stem mora. And again we find that ～さ serves to lengthen the adjective in order to let ～そう（な）appear:
g. そういう提案は無さそうだ。 Such a proposal doesn't seem to exist. h. 経験のあまり無さそうな人 a person who doesn't seem to have much experience
Then there is, of course, also the negation suffix ～な（い）, which also has only one stem mora. Personally I do insert ～さ but that may be considered substandard (see here). Still I'd say this:
i. 彼は来なさそうだ。 He doesn't seem to come. j. 彼は来なさそうなタイプだ。 He's the type who doesn't seem to come.
And the people in my environment, who all happen to be Japanese, do so, too.
Firstly, I searched Balanced Corpus of Contemporary Written Japanese (BCCWJ, http://www.kotonoha.gr.jp/shonagon) and all results were either
- そうさ (as in そうだよ)
- ごち そうさ ま
- そうさ せる and its conjugations.
Here is why I think ～そう+さ as you suggested cannot exist. It would consist of two parts, where
～さ is describing a quality, an objective fact about someone/something
～そう is describing a feeling, a subjective assessment of someone/something
By some general principle in Japanese of subjective feelings being orthogonal to objective facts (see this question: When to use 欲しがる instead of 欲しい), you cannot combine そう and さ. Grammatically, そう works just like other na-adjectives, so there's no syntactical reason to assume you can't append さ to it. This is a semantic obstruction.