本拠 and 住居: a base of activity and a dwelling
Compare a survey base used by an expedition with a dwelling being sought near a company, retaining each place's role and the ongoing search.
A place serving as 本拠
本拠（ほんきょ） means a base or headquarters. 「探検隊は海辺の町を調査の本拠とした。」 says that the expedition used the seaside village as a base for its survey. 調査の identifies the activity supported by that place.
「この球団は北部の都市に本拠を置いている。」 says that the team has its base in a northern city. It identifies the team's base without stating that every member lives there.
A 住居 being sought
住居（じゅうきょ） means a residence or dwelling. 「会社の近くで住居を探している。」 describes looking for a place to live near the company. A dwelling is the object of the search.
探している presents an ongoing search. It does not report that a dwelling was found or a move completed, and being near the company does not establish a base of activity.
The role assigned to a place
The 本拠 examples concern bases for a survey or a team. The 住居 example concerns a place to live. One place can serve as both a base and a dwelling.
The words alone do not establish the number of bases or a dwelling's legal address. The activity associated with the place and the search for somewhere to live explain their roles.
Does 「会社の近くで住居を探している。」 say that a dwelling has already been found and made a base of activity?
Show the answer and why
No. It presents an ongoing search for a place to live near the company. Finding the dwelling or making it a 本拠 is not stated.