The transferring employee is authorized for a specific employer and the assignment described in the petition, so changes require legal review. A spouse in valid L-2S status is employment authorized incident to that status rather than through a particular job, which is a different legal basis, not a lesser one.
Do not reason from the principal to the spouse
Households often assume the dependant faces the same employer restriction and turn down suitable work as a result. The accurate position is that the spouse's authorization depends on holding valid status, while the principal's depends on the approved employment. Both can end together if the underlying status lapses, and that is the point where the two timelines genuinely connect and where advice should be sought promptly.
There is a further asymmetry worth understanding, because it cuts the other way. The transferring employee's position is restricted but stable: it is tied to an approved employer and assignment, and it does not change because a project evolves, provided the assignment remains what was approved. The spouse's position is broader but derivative: it permits work for any employer, and it ends if the underlying status does.
A household planning around two incomes should understand that the second one carries the risk attached to the first, which is an argument for raising any change in the principal's employment promptly rather than treating it as an internal matter.