The　delay-sensitive　and　resource-limited　natures　of　multi-access　edge　computing　(MEC)　applications　make　it　necessary　to　offload　local　tasks　to　nearby　MEC　servers.　Large　amounts　of　offloading　data　are　transferred　among　MEC　servers　within　the　stringent　deadline　constraints.　The　offloading　system　hence　needs　to　deliver　the　data　over　end-to-end　(E2E)　connections　as　soon　as　they　arrive.　However,　traffic　fluctuations　make　the　offloading　system　difficult　to　provision　the　required　bandwidth　over　the　E2E　connections　and　guarantee　the　deadline.　In　this　paper,　we　present　a　storage-enabled　adaptive　multi-path　scheduling　method　(SAM)　for　offloading　transfers　across　the　optical　metro　network.　Instead　of　delivering　the　whole　data　across　a　single　path,　SAM　can　adaptively　split　the　data　into　small　segments　and　route　them　through　multiple　paths.　This　not　only　improves　the　throughput,　but　also　enables　large　time　windows　to　schedule　segments　on　their　own　paths　within　the　given　deadline.　With　the　large　time　window,　SAM　can　leverage　MEC　storage　to　temporarily　store　the　segment　at　the　intermediate　servers　when　provisioning　the　entire　E2E　path　fails.　Studies　show　that　compared　with　the　state-of-the-art　scheduling　methods,　SAM　can　accommodate　more　transfer　requests,　shorten　delivery　time　and　accelerate　offloading　transfers　efficiently.　SAM　is　beneficial　to　task　offloading.