Catalysis of the reaction: 3',4',5-trihydroxy-3,7-dimethoxyflavone + S-adenosyl-L-methionine(1+) = 3',5-dihydroxy-3,4',7-trimethoxyflavone + S-adenosyl-L-homocysteine + H+.
S-adenosyl-L-methionine:5,3\',4\'-trihydroxy-3,7-dimethoxyflavone 4\'-O-methyltransferase activity