Possible, but unlikely. Bitcoin is permissionless. Trying to make all miners adhere to a single plan is akin to herding cats. That said...

The most widely discussed plan os to achieve >= 75% of solved blocks, hold that until the next difficulty retargeting (0-2 weeks), hold it for an entire difficulty retargeting, then start building blocks larger than 1MB (soft cap at 2MB seems to have some support).

Again, it is possible that some miner jumps the gun. However, he is likely to find his blocks orphaned no only by the stragglers, but also by BU miners that are executing according to the new plan.

There is the possibility that a new plan emerges. I've not heard of such.

With this, the minority (legacy) fork will drop from being capped at ~250,000 tx/day to about 62,500 tx/day, leading to a near-stall. If more miners defect to BU at that point (which would be in their financial interest due to the slow rate), the minority fork may rapidly dwindle down to a hard core of the obstinate 1% true core believers. Which of course, will slow the minority fork even further. It may never make it to the next difficulty retargeting, when the rate could be (partially) adjusted. In no way would the retargeting occur before two months.

The BU fork (assuming 2MB soft cap) would be capable of processing ~250,000 tx/day * 2MB/1MB * 75% = ~375,000 tx/day (more if further defection) until the next difficulty retargeting - in about 20 days (less if further defection), where it would jump to ~500,000 tx/day (more if further defection).

The upshot is that the minority fork will be economically irrelevant. This will create market pressure to consider the majority fork 'The Real Bitcoin', and the minority fork 'that other bitcoin-like alt'.

Accordingly, it would not rip the network in half, more like 99%/1% -- if that.