interferance question

This is all hypothetical:

Let's say I have an 802.11 AP and a client or two or three. Let's say that
a neighbor's phone or other device interferes. Let's also say I don't want
to change my channel.

Would increasing my send/receive power from both the client(s) and AP
(either via higher gain antennas or via signal booster) likely clear up the
problem by "overpowering" the weaker interfering signal from the neighbors
phone? Or, would using a booster or higher gain antennas only increase the
interferance by also increasing my "receive power" ('sensitivity' or
whatever the proper terminology is)?