Can I extend my multi-entry visa in Thailand now, a week after entering?

In Phuket, Chang Mai and Bangkok you can apply for a 30 day Extension of Stay 45 days before, in Jomtien Pattaya it is 15 days before and all other Immigration Offices allow this 30 days before till your last day of Admitted to Stay.

I believe Chiang Mai is 45 days before your "admitted until" stamp. So you will have to wait 15 days from entry if you got a 60 day stamp. You can extend a METV entry in any province, if you are travelling somewhere else in Thailand, you don't have to come back to Chiang Mai to extend it. It's only non-immigrant visas you NEED to extend in a particular place, tourist visas you can extend anywhere.

Different provinces have different rules as to how early you can extend, the shortest I think you have to wait until 15 days before expiry. You need to check this for the specific office you want to use before you go there.

I do not understand what you try to ask. Where do you stay and where do you like to travel to?