Cloud Chamber, the firm commissioned by 2K Games to develop a new game in the series BioShock, is currently looking for various professionals, as written in his Official site. Job descriptions seem to confirm at least two things about this possible BioShock 4: what it will be openworld and that, like most open world games, will have both primary and secondary missions.
The role description of senior writer is the one that practically seems to confirm these elements:
“We hope to find someone who can weave impactful and character-based stories in an open world environment. […] Will think of primary and secondary missions with design ”.
Furthermore, experience with U is considered "Strongly desired" while much emphasis is placed on BioShock having a "live" world. And indeed the Senior World Designer must "Design and create bespoke missions that bring the game to life."
Al AI programmer you are asked to create "A vision for a significant urban crowd system" and will have to "Push the limits of what is possible with interactive crowd systems".
Of course, there is a possibility that whatever Cloud Chamber is currently preparing may change dramatically during development, and given the nature of some of these roles, it seems development is nowhere near release. In short, we just have to wait.