shine up to (?.)

• act up to
• agree to anything
• approach
• break the ice
• brown-nose
• court
• cultivate
• curry favor
• dance attendance on
• fall all over
• fall over
• fawn upon
• handshake
• make advances
• make court to
• make up to
• pay addresses to
• pay court to
• play up to
• polish the apple
• run after
• suck up to