Can I issue a section 21 after issuing a section 8?

We have an HMO, in which a tenant has not paid for over 3 months, he has had a months notice to pay prior to being issued with a section 8. He has still not moved out or paid any of the rent owed, so am about to start court proceedings. What I would like to know is, is it possible to also serve a section 21 and see which route is quickest in getting the eviction notice or should I now stick with the section 8 and attempt to get some of the money owed at the same time?

Thanks