Curious if this is a possibility
Yes, you can get admitted with many different majors. Look up some MS programs on what they look for in admissions, and they will usually state exactly which majors and courses they expect someone to have had. The courses are more important than the name of a major. Then you can be sure to put together a planned major, minor and electives to meet the requirements of your target MS programs. If you lack specific courses, you can often still be admitted to an MS program but required to make up the deficiencies by taking the courses after admission.
Sample admissions info for MS in Petroleum Engineering at USC:
APPLICATION CRITERIA
An undergraduate degree in Petroleum Engineering (or other engineering, math, or hard science with assigned deficiencies) from a regionally accredited college or university.
Deficiency Courses: Students without a B.S. in Petroleum Engineering must complete the following prerequisite courses at USC: Introduction to Transport Processes in Porous Media (PTE 411x), Petroleum Reservoir Engineering (PTE 412x), Formation Evaluation (PTE 461), Petroleum Geology (PTE 466), and Computational Reservoir Modeling (PTE 500) before beginning the M.S. program. Units from these courses cannot be applied towards the degree. Other prerequisite courses may be assigned on a case-by-case basis upon consultation with the Department Advisor.
Satisfactory cumulative undergraduate GPA (grade point average)
Satisfactory GRE and TOEFL test scores. All scores must be officially reported to the university directly by ETS.
Satisfactory performance in previous coursework related to the intended major.