A versatile, multi-port, intubation-permitting oxygen mask is provided including two diaphragms (nasal and oral) each configured with a continuous, flexible, modifiable membrane from which an instrument-access port may be manually constructed, when and if needed. The novel oxygen mask preferably includes a multiple-inlet port having a standard oxygen tube connector and an interchangeable breathing-therapy device connector, a carbon dioxide sampling port, an exhaust port, and a nose clip. The mask can be worn as a standard oxygen mask during traditional oxygen therapy, yet quickly converted into an intubation mask. The clinician manually perforates the nasal and/or oral diaphragm to create a point and size of entry perfectly matched to the requirements for a variety of procedures that may be performed involving nasally or orally introduced scopes or probes—without disturbing the ongoing benefits of increased oxygen saturation and continuous monitoring of expired gases.