都可以。suggest to do和suggest doing的区别：含义不同、用法不同、强调重点不同。suggest to do的含义为“建议这么做”，侧重于建议两个人一起做某事;suggest doing的含义为“建议做…”，侧重于建议接受者自己去做某事。
suggest to do的含义及用法
suggest to do意为建议这么做，建议两个人一起做某事。
例句：Can you suggest any means to do it?
你能不能给我想个什么办法做这件事?
Can you suggest a way ( to do it)?
你能提出一个办法吗?
I suggest a method to do on the web page changes, in order to improve the level of the key pages.
我建议在某个方法上对网页做些变化，以此来提高关键页面的等级。
suggest doing的含义及用法
suggest doing意为建议做，建议接受者自己去做某事。
例句：I suggest doing it for five minutes at a time.
我建议每次锻炼5分钟。
You also use "couldn't" in a question to suggest doing something.
用在疑问句中也可用以建议做某事。
If there's something you want to do or somewhere you want to go, we suggest doing it solo.
如果有什么事你想做或什么地方你想去，我们建议单独行动。
I'd probably suggest doing a lot of different things to keep their interest.
我会做一些事情让她们保持对健身的兴趣。
I suggest doing this in the company of friends, family members, therapists, coaches, or all of the above.
我建议在朋友、家人、医疗师、教练或全部人一起的陪同下。