... to be on the pitch at the point where he stepped off. There are some other nuances here but I didn't see the play and don't have time to look at the rules.

I believe when the player runs off the field like that he has taken himself out of the play and technically the referee needs to give him permission to return to the field of play.

... offside rule is that the attacker who steps over the end line is deemed to still be on the field at the point he stepped off.

I had to revisit the FIFA book to jog my memory.

In this case though the player running over the goal line has effectively taken himself out of the play and though he is in an offside position should not be called for offside since he is no longer engaged in or influencing the play.

I'm specifically asking can he influence the ongoing play by coming back onto the pitch in the case that 2 defenders also overran the endline with him.

By definition, as I was taught again, if a player leaves the field via a goal line he is deemed to be on the field at the goal line. In the case of an offensive player whose momentum carries him over the goal line and two defenders cross over as well, the player could probably return and be onsides since the two other defenders are deemed to be on the field on the goal line.

If you're within a step of the goal line, the referee isn't going to penalize you for returning to the pitch. If the attacker has run to the ad board because he chose to and became a spectator, he should be booked for leaving the field of play without permission from the referee and cannot return until beckoned. But being run off the pitch because you're chasing a loose ball, for example, isn't an issue. That's just normal play. Walking off is different.

That happens quite often, and it's just considered to be the normal course of play.

Don't overthink the impact to offside in this scenario. If you're off the pitch beyond the goal line, you're considered to be ON the goal line w/r/t offside positioning. However, you obviously cannot impact the play if you're off (unless you're just off, then you can, in theory). If you come back on, you can clearly impact the play.

If you step off, you're considered to be standing right on the end line - for either side. Now, if an attacker steps off and avoids impacting the play, then he's avoided impacting the play and the fact that he stepped off is irrelevant.