Rabbitbait
Grog-nerd
5e's Tomb of Annihilation was absolutely brilliant and might just be the best campaign I have run, but did not really have much room for personalisation. Yes you could insert side-quests, but given that the majority of the adventure is coming across trouble in the jungle it does not leave a lot of room for a characters back-story to come into play. There is a lot you can do at the start before you go into the jungle, and probably a bit in the lost city of Omu. Once you are in the tomb itself there isn't really any opportunity to insert anything else.Unfortunately, I can’t speak to 5E‘s Tomb too directly (or 4E for that matter) - I’ve had an awful experience with the former and none with the latter - but with a large portion of it being a hexcrawl, I don’t think it allowing for side ventures is a bad thing, as long as it doesn’t feel incomplete and leaving the DM out to dry with large gaps of “and something happens, make it up until the party is X level”… and then the book picks up with the next part of the story.
HOWEVER - the campaign is brilliant for providing little self contained adventures that can be pillaged for use in other campaigns.