Would it be possible to make a room (which is an existing extension) bigger by extending the extension??!!

It is certainly possible, even quite common. there are planning issues to address first-regarding size etc. Regards Simon

Extending previous extensions is quite common. With certain provisos yo can extend 3 metres out from the back of the original house without planning permission and 4 metres on a detached property. any more than that would need planning consent and would depend on the effect it would have on your neighbours.