Can we certify the commercial portion only of a mixed use building (residential & commercial) under LEED BD+C ?

It depends. Check out the LEED rating system selection guidance https://www.usgbc.org/leed-tools/rating-system-selection-guidance and MPR Must use reasonable LEED boundaries https://www.usgbc.org/credits/new-construction-existing-buildings-commercial-interiors-core-and-shell-homes-mid-rise-sch-1

Note the following that I believe will pertain to your project: 

• Homes and residential buildings that are greater than six stories use LEED BD+C. 
• Buildings that are physically connected by programmable space are considered one building for LEED purposes unless they are physically distinct and have distinct identities as separate buildings or if they are a newly constructed addition. If separated, the projects should also have separate air distribution systems and water and energy meters (including thermal energy meters).