Hmmm. It's been a while since I thought about lipid chemistry, but I think we could imagine such a thing. It would need a method of automatically partitioning itself without spilling its guts everywhere. I bet we could dream one up where some environmental change triggers such a partitioning. However...
If the cell simply kept growing, it would eventually break up automatically.
...do you mean our hypothetical cell, or do you mean that extant cells will behave this way?