The answer to the title question, "Is it possible for a person who has faith in Jesus to only receive “a measure of salvation” as opposed to “full salvation”?" is no, at face value. Salvation, at it's very heart, is an event: We enter the Ark of God's salvation and are sealed within by the grace of God:

For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit: By which also he went and preached unto the spirits in prison; Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water. The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ: - 1 Peter 3:18-21

One is translated from the kingdom of darkness unto the kingdom of light upon a transition of belief from "not Christ" to Christ.

From that time Jesus began to preach, and to say, Repent (change your mind): for the kingdom of heaven is at hand. - Matthew 4:17

Giving thanks unto the Father, which hath made us meet to be partakers of the inheritance of the saints in light: Who hath delivered us from the power of darkness, and hath translated us into the kingdom of his dear Son: - Colossians 1:12-13

Then said Jesus again unto them, I go my way, and ye shall seek me, and shall die in your sins: whither I go, ye cannot come. Then said the Jews, Will he kill himself? because he saith, Whither I go, ye cannot come. And he said unto them, Ye are from beneath; I am from above: ye are of this world; I am not of this world. I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am he, ye shall die in your sins. John 8:21-24

We are, as the Scripture says, born again, not of the flesh but of the Spirit and we have passed from death unto life:

For the Father judgeth no man, but hath committed all judgment unto the Son: That all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him. Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life. - John 5:22-24

For sure there is a process to undergo: A saved (new-born) individual is not what they will ultimately become:

Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is. - 1 John 3:2

We must be sanctified. The Spirit lusts against the flesh and the flesh lusts against the Spirit:

For the flesh lusteth against the Spirit, and the Spirit against the flesh: and these are contrary the one to the other: so that ye cannot do the things that ye would. - Galatians 5:17

But the ultimate victory of this struggle is guaranteed to us in Christ:

Now unto him that is able to keep you from falling, and to present you faultless before the presence of his glory with exceeding joy, To the only wise God our Saviour, be glory and majesty, dominion and power, both now and ever. Amen. - Jude 1:24-25

For the which cause I also suffer these things: nevertheless I am not ashamed: for I know whom I have believed, and am persuaded that he is able to keep that which I have committed unto him against that day. - 2 Timothy 1:12

The one who is able is also trustworthy:

Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ: - Philippians 1:6

This is an irrevocable transaction:

All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out. For I came down from heaven, not to do mine own will, but the will of him that sent me. And this is the Father's will which hath sent me, that of all which he hath given me I should lose nothing, but should raise it up again at the last day.  And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day. - John 6:37-40

Salvation is not merited by our own efforts and it is neither retained by either our will nor our skill:

For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. - Ephesians 2:8-9

Now unto him that is able to do exceeding abundantly above all that we ask or think, according to the power that worketh in us, Unto him be glory in the church by Christ Jesus throughout all ages, world without end. Amen. - Ephesians 3:20-21

For it is God which worketh in you both to will and to do of his good pleasure. - Philippians 2:13

I think, for all of us, this question veers off into the bailiwick of assurance of salvation. John's first epistle is all about evaluating where we stand (personally) in the faith by the standard of love:

If a man say, I love God, and hateth his brother, he is a liar: for he that loveth not his brother whom he hath seen, how can he love God whom he hath not seen? - 1 John 4:20

The purpose statement of John's first epistle is:

These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life, and that ye may believe on the name of the Son of God. - 1 John 5:13

Everything in 1 John is directed towards those who have believed and who have eternal life and need to be assured of it so that their belief may deepen.

Seen in this light, "partial salvation" vs. "full salvation" is more of a matter of degree of experiential personal assurance. If one measures their salvation based upon the performance of another (mere human) one becomes trapped by works. If one measures their salvation based upon the performance of Christ, both without and within, one is set free and assured by both mercy and grace.