They became more serious为主语+系动词+表语结构啊！！！

become为变化系动词

However ,after  a year so in which they became more serious about their work, the Monkees started to play and sing their own songs like a real band.

然而，在一年后，他们变得更加认真的工作，猴子开始演奏和唱自己的歌曲，就像一个真正的乐队。