Can Shanghai and Hangzhou pay social security at the same time?

Excuse me, are they all basic pensions for employees? You just have to hand it over. If you have a Hangzhou hukou, you only need to pay in Hangzhou before the legal retirement age, and you can transfer your Shanghai hukou to Hangzhou. If you are in Shanghai, you can ask what the local retirement in Shanghai requires for the social security transfer in Hangzhou. Generally, it doesn't turn so fast, so it's safer to do it three or four months in advance. At least your time in Hangzhou is not cumulative. You can stop reporting in Hangzhou, and Hangzhou will keep your account record.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.