有get to doing吗？

get doing ＝start doing指“（主语）开始做……?，即主语是doing表示的动作的执行者。例如：

They went in and got chatting together．他们走进去，开始攀谈起来。

get done的意思是“（主语）被……?，表示被动的意思，即主语是done表示的动作的承受者。例如：

Don't get caught in the storm．别赶上暴雨了。

get to do表示“由……变为；经过一过程或努力而……?，to do这个动作是主语发出的。例如：

They got to know her two years ago．他们是两年前认识她的。

可以说get to do，没有get to doing，但是有两个特例。

get to do something
非正式用法
to have the opportunity to do something:
有机会去做某事

We got to meet all the stars after the show.
She gets to travel all over the place with her job.

get to thinking/wondering something
非正式用法
to start thinking something:
开始思考，计划某事

He got to thinking how disappointed his parents would be.