Basis for belief that a person can be "possessed by" a demon?

There are several different forms of verbs used in the New Testament translated as possessed. You seem to be conflicting between these two:

δαιμονίζομαι

daimonizomai.....dahee-mon-id'-zom-ahee

Middle voice from G1142; to be exercised by a daemon: - have a (be vexed with, be possessed with) devil (-s).

Total KJV occurrences: 13

And this one:

ὑπάρχοντα

huparchonta....hoop-ar'-khon-tah

Neuter plural of present participle active of G5225 as noun; things extant or in hand, that is, property or possessions: - goods, that which one has, things which (one) possesseth, substance, that hast.

The following Scriptures will help to define these verbs.

Acts 4:32 through 35 Now the multitude of those who believed were of one heart and one soul; neither did anyone say that any of the things he possessed was his own, but they had all things in common. 33 And with great power the apostles gave witness to the resurrection of the Lord Jesus. And great grace was upon them all. 34 Nor was there anyone among them who lacked; for all who were possessors of lands or houses sold them, and brought the proceeds of the things that were sold, 35 and laid them at the apostles' feet; and they distributed to each as anyone had need.

In these Scriptures the verb ὑπάρχοντα is used and actually is more restricted to material object possession.

in these Scriptures the verb phrase δαιμονίζομαι is used:

Mark 5:1 through 13 NKJV Then they came to the other side of the sea, to the country of the Gadarenes. 2 And when He had come out of the boat, immediately there met Him out of the tombs a man with an unclean spirit, 3 who had his dwelling among the tombs; and no one could bind him, not even with chains, 4 because he had often been bound with shackles and chains. And the chains had been pulled apart by him, and the shackles broken in pieces; neither could anyone tame him. 5 And always, night and day, he was in the mountains and in the tombs, crying out and cutting himself with stones. Mar 5:6 When he saw Jesus from afar, he ran and worshiped Him. 7 And he cried out with a loud voice and said, "What have I to do with You, Jesus, Son of the Most High God? I implore You by God that You do not torment me." 8 For He said to him, "Come out of the man, unclean spirit!" 9 Then He asked him, "What is your name?" And he answered, saying, "My name is Legion; for we are many." 10 Also he begged Him earnestly that He would not send them out of the country. 11 Now a large herd of swine was feeding there near the mountains. 12 So all the demons begged Him, saying, "Send us to the swine, that we may enter them." 13 And at once Jesus gave them permission. Then the unclean spirits went out and entered the swine (there were about two thousand); and the herd ran violently down the steep place into the sea, and drowned in the sea.

And these two Scriptures are the ones of interest since the verb phrase is used:

Mark 5:15 and 16 NKJV Then they came to Jesus, and saw the one who had been demon-possessed and had the legion, sitting and clothed and in his right mind. And they were afraid. 16 And those who saw it told them how it happened to him who had been demon-possessed, and about the swine.

While English is a noun based language Greek is a verb based language, that is why there are differences in the verbs and verb phrases used.

The verb phrase δαιμονίζομαι is used which is actually daimonizomai which is defined by Thayer as:

δαιμονίζομαι

daimonizomai

Thayer Definition:

1) to be under the power of a demon.

Part of Speech: verb

There are many different extents to which a person can be possessed by demons as is indicated here in that the demon answered with one voice but professed to be many demons.

and they have varying control over the person as is indicated in the following Scriptures:

Matthew 12:22 NKJV Then one was brought to Him who was demon-possessed, blind and mute; and He healed him, so that the blind and mute man both spoke and saw.

Acts 16:16 NKJV Now it happened, as we went to prayer, that a certain slave girl possessed with a spirit of divination met us, who brought her masters much profit by fortune-telling.

As far as to what extent a demon can control it's host is not made totally clear, but it is obvious that it can completely change the hosts as is indicated by Mark chapter 5 where the one possessed by Legion acted completely foreign to his normal self.

Sorry I cannot give you more specifics, but I hope this gives you enough to continue your study.