I mean have there ever been some book, audio, comic storyline, or even tv episode, that we are greeted with The Doctor, and he must go save his previous companions from regenerations past. This isn’t referring to the special episode in Sarah Jane Adventures where Matt Smith appears though.
This basically happens in "The Five Doctors," the twentieth anniversary show. The First, Second, Third, and Fifth Doctors all make major appearances, along with quite a few companions. Susan, the Brigadier, and Sarah Jane Smith have substantial roles, along with the then-current companions Tegan and Turlough. Jamie, Zoe, and Liz also appear as projections to throw the Doctors off the trail as they all play the Game of Rassilon. (Jamie and Zoe are recognized as fake when a later Doctor remembers that their memories of the time they spent traveling in the TARDIS were wiped at the end of "The War Games.")
There is some swapping of companions from incarnation to incarnation as the story goes on. Sarah Jane Smith is quite surprised to see that the Third Doctor is back when she meets him. The First Doctor, when he reaches the TARDIS, has a brief confrontation with the Fifth Doctor's companions about just whose TARDIS it is. It is interesting to see the Doctor's associates having to interact with different regenerations than they are familiar with. It also continues the gag introduced in "The Three Doctors" of the various Doctors not getting along.
There is also "The Two Doctors," with the Second Doctor guest starring alongside the then-current Sixth. Jamie also appears, in a major role this time. After the Doctor and Jamie are separated early on, the Sixth Doctor eventually rescues him after Jamie has evidently spent a considerable amount of time on an abandoned space station. This may have been done in part as a way of explaining Frazier Hines' much older appearance. Unfortunately, while it has some interesting moments (and a higher budget than usual), the story is not very good. It is riddled with poor costuming and continuity errors and saddled with a heavy-handed moral about how eating meat is like murder.
What you have described in your question and comments - wanting to see "how would these companions react to a different man calling himself the Doctor" - basically happens in any of the "multiple Doctor" TV episodes:
- The Three Doctors
- The Five Doctors
- The Two Doctors
- The Day of The Doctor
In pretty much all of these episodes we see the companions deal with seeing a different incarnation of The Doctor to the one they travel with.
From The Two Doctors:
JAMIE: He's not the Doctor I know.
DOCTOR: I am too, Jamie McCrimmon. I am another aspect of him, just as he is of me.
DOCTOR: I was him, he will be me.
JAMIE: Who will I be?
We also saw Sarah Jane's reaction when she realised who the Tenth Doctor was in School Reunion:
DOCTOR: Hello, Sarah Jane.
SARAH: It's you. Oh, Doctor Oh, my God, it's you, isn't it. You've regenerated.
DOCTOR: Yeah. Half a dozen times since we last met.
SARAH: You look incredible.
The Eleventh Doctor appeared in The Sarah Jane Adventures episode Death of The Doctor in front of Sarah Jane and Jo Grant:
DOCTOR: Hello, Sarah Jane.
SARAH JANE: Doctor.
RANI: That's the Doctor?
JO: What Doctor? The Doctor? My Doctor?
SARAH JANE: Yeah, well, he can change his face.
JO: I know, but into a baby's?
I am not familiar with all extended universe media, but there are The Companion Chronicles on Big Finish audio productions that have brought various companions together. The episode Dumb Waiter brings together Jamie and Leela, for example, but some of these stories do not include a portrayal of The Doctor.