As you know, Trinitarians believe that while there's only one God, the Godhead consists of three distinct persons - the Father, Son, and Holy Spirit.
All are said to be *equally* omniscient, omnipotent, omnipresent, eternal, and unchanging.
If this is the case, then there is no place in which the Holy Spirit does not dwell. If he is within you, for example, but not within me, then he is finite.
Blessings.