As usual, your questions are few in words and full of meaning.
Like with all the Prophets, their language is usually not to be taken in a literal sense, but rather in an allegorical sense.
In this case, the stone mentioned is referring to a particular King destined to lead the nation of Israel. This is in keeping with both Targum Yonatan and Radak to this line. In the context of Isaiah (the Prophet of the final redemption) in general, this means Melech HaMoshiach.
Rabbi Chiya to Yerushalmi Yoma 27a:3 compares this King to the Foundation Stone in the Holy of Holies of the Temple in Jerusalem, the stone upon which the Ark of the Covenant (which contains the tablets of the ten commandments) rests.
The key to addressing your particular question (does this stone pertain to the whole building or just a single corner) relates to understanding the concept of foundation (יסד ,מוסד or יסוד) from the Hebrew used by the Prophet.
This is picked up on in the commentary of Metzudat David who explains that this particular King will be like the ultimate example of a Foundation (יהיה כהיסוד המיוחד שביסודות).
And this points to the concept of Yesod, meaning Foundation, as used in this context.
This refers to a Kabbalistic concept pertaining to the ten Sephirot (Qualities by which the structure of all creation is established and operates. Discussion of this subject can be found in Sefer Yetzirah, for example, and many other sources.). The ninth of these sephirot (if going from above to below) is called Yesod and is described in terms of function as the vehicle which makes it possible to connect and become one with G-d's Kingship (מלכות).
Just to emphasize, the connection is with G-d's Kingship, meaning how G-d's dominion is revealed within all of His creation. This is what Melech HaMoshiach (King Messiah) enables.