I suggest doing it in another way.

我建议换一种方式做这件事。

I suggest doing it a different way.

我建议以另一种方式做这事。

I suggest doing it in a different way.

我建议用不同的方法做。

May I suggest doing it in another way?

我建议换一种方式做这件事如何？

D. suggest doing STH.

意为“建议做某事”。