Contact an entertainment company that represents both bands and DJs and discuss the option of hiring a DJ and a singer plus an instrument or two to play for part of the reception.
You can have a singer, accompanied by a keyboard and/or guitar and/or horn instrument, to sing and play the music for special dances. Another option is to have live music, such as standards, being sung during dinner instead of canned music and have the DJ play music that gets the crowd on the dance floor.
Be honest about your budget and what you want for your wedding and the vendors you’re meeting with will better be able to help find the right solution for you.