As a rule, no – you should expect to share a room whilst trekking to Everest Base Camp.
There are two main reasons for this.
Firstly, symptoms of altitude-related illness often develop during the night. Sharing rooms helps ensure that any problems are noticed quickly, allowing guides or teammates to respond if someone becomes unwell.
Secondly, most teahouses along the Everest Base Camp route offer twin or shared rooms rather than single occupancy rooms. For this reason, even with a supplement we cannot guarantee single rooms.
If you are travelling with a friend or partner you will share a room together. For those joining a group, we arrange room sharing on a same-sex basis and, where possible, try to pair people of a similar age.