The Partial Rapture Theory isn't really a matter of timing, it can overlap with any of the other views. It is sometimes linked to an idea that more then one Rapture will occur and thus they might all be right. Some people believing a from of this I know are mainly Mid-Trib in their timing, so I feel the need to make sure people know this isn't a view I agree with.
The Partial Rapture Theory is that not all of the Saved alive on Earth at the time are Raptured at the Rapture, or at least not the first Rapture. Only those who are the most Obedient and Faithful.
My views on Soterology and Ecclesiology could be viewed as lending themselves to this view. I believe firmly in Eternal Security, yet I disagree with Calvinists and others who say they believe in Eternal Security but then turn around and say "if you are really saved you won't ______" whatever their line is.
I believe that like the Prodigal Son a Believer can squander their Inheritance but will never lose their Sonship. I recommend Chuck Missler's studies on Eternal Security, including Hebrews 6. Though I disagree with him on a few verses concerning Predestination where he sounds like he unwittingly agrees with the Calvinist view, but those are minor.
When Jesus in Matthew refers to the "Outer Darkness" that's not Hell. Revelation 21:25-27 tells us that not everyone living in the New Heaven and New Earth will be in New Jerusalem. And that some won't be allowed to enter it. That's the "Outer Darkness" Jesus was referring to (because the context was clearly describing saved individuals, only the Saved are his servants), being outside New Jerusalem.
So some people when responding to certain views on Rewards tie in a disapproval of any notions that all Christians aren't equal at the Bema Judgment. I believe we should not be Judging each other during our life on Earth, but it's clear in Eternity there will be distinctions.
BUT, that differentiation happens at the Bema Seat Judgment, and thus after The Rapture. So it does not exclude anyone from The Rapture. We are during our life on this Earth all part of the Body of Christ regardless of our obedience or faithfulness.
Some who agree with my view that the 144,000 are part of The Church and that they are Raptured in Revelation 14, will add that only the 144,000 are Raptured. As I've said in other posts on that subject, they are a specific group that represents the whole.
I've said before that not all saved are part of The Church. A related question to that however is, are all saved during the Church Age part of The Church? While we're alive, yes. I believe we're all The Body of Christ. But after the Bema Seat Judgment, I do think it's possible some of us will lose our opportunity to be the Bride of Christ.
The Ten Virgins Parable of Matthew 15:1-13 is one Bible passage that could be used to support a Partial Rapture. Actually the way Partial Rapture supporters interpret this is kind of the natural conclusion of the way Pre-Tribbers use it. (That the Five Virgins taken represent those who hold the Pre-Trib view, and others those who do not). Problem is, what Jesus tells the Foolish Virgins "I know you not" is how other Eschatological passages from Jesus define the unsaved. Yet Pre-Tribbers don't usually want to say they think your not saved if your not Pre-Trib, but that seems to be the implication of their attitude sometimes.
Pre-Tribbers often forget that parables are not always what they seem.
I don't think this Parable is about the timing of the Rapture, or that the difference between the groups has anything to do with their theory on it's timing being correct or not. Christ's offer to be his Bride is extended to all Humanity, but only the Saved are prepared to be ready to accept it when he comes. Because the Saved have the Light of the World in us, our Lamps won't go out.
The Letters to the Seven Churches can also be used by Partial Rapture theorists. Mainly the messages to Thyatira and Philadelphia. Where certain statements make it seem like the former is told they will go into the "Tribulation Period" and the latter they will not.
To Thyatira he says of "Jezebel" and those committing Whoredom with her "Behold, I will cast her into a bed, and them that commit adultery with her into great tribulation, except they repent of their deeds." Thing is, in my Great Tribulation study I show that it isn't a specific time period at all, it refers to all Persecution the Church has faced.
To Philadelphia he says "Because thou hast kept the word of my patience, I also will keep thee from the hour of temptation, which shall come upon all the world, to try them that dwell upon the earth." This is often used against Post-Trib in general. One Question is, if this is about the Rapture, does it being only in Philadelphia's message mean it applies only to Philadelphian Christians? The Promise for the Believer parts of the other Letters seem to embody many things characteristic of all Believers, so no I don't think so.
But also it this really Rapture relevant?
This Verse doesn't use Wrath or Tribulatio, or Day of The LORD. It says Hour of Temptation. I'm reminded of how in the Lord's Prayer, we're instructed to pray that we are lead not into Temptation and delivered from Evil. And in Matthew 24:24 Jesus says "For there shall arise false Christs, and false prophets, and shall show great signs and wonders; insomuch that, if it were possible, they shall deceive the very elect." The key complication is that it isn't possible. I don't think this means we're immune to being tricked in general. But once the Abomination of Desolation happens, things will be crystal clear to those with the Holy Spirit.
So neither of those two passages from the letters to the Churches I view definitively as Rapture relevant.