Yes, if you want to stay more than 30 days with visa in Sri Lanka you may apply for an extension once you are already in the country. The visa may be extended up to 90 days from the date of arrival at the first instance and further 90 days at the second instance.
We suggest that all customers apply for their electronic visa now (valid for 30 days) and then extend it while you are in Sri Lanka. Apply here: https://www.srilankavisaonline.com
NOTE - Application for an extension should be submitted to the Visa Section of the Department of Immigration in Sri Lanka (head office**) by visiting the Department or through an Authorized Agent.
**Department of Immigration and Emigration
41, Ananda Rajakaruna Mawatha,
Colombo 10, Sri Lanka