North America’s two dominant oil companies are carving divergent paths as the global crude market staggers toward what’s widely expected to be a hefty supply glut.

Exxon Mobil Corp. is pressing ahead with a raft of expansion projects, even as OPEC and its allies increase production and oil futures hover near a four-year low. Chevron Corp. meanwhile is positioning itself to wring cash from existing operations to weather the market downturn.