I questioned a local player standing on his partner's side when I was serving to his partner. The rule is 9.5 In doubles, during the delivery of service (Law 9.2, 9.3), the partners may take up any positions within their respective courts, which do not unsight the opposing server or receiver. I assume 'their respective courts' means left and right, and therefore you can't be standing in the area that is served to.
"Respective court" means the whole court on the side of the player. The area been served to called "serving court"..
As @stradrider correctly pointed out, this means everything on their side of the net. In doubles, the partners are always standing in the center:
