@providencejim Is it perfectly correct English? I may be behind on this issue, but since when do collective nouns take plural verbs? That just sounds horrible. It is definitely not accepted in the spoken or written mainstream of the states or Canada as far as I know. Is there maybe a distinction between collectives that are mass vs. quantity groups? For example, if I lose one apple of the four I have, I have "fewer" apples, but if I spill some applesauce from the jar, I have "less" applesauce.

For the sake of academic argument alone, I would only venture to guess that this would be the correct form for that sentence: "That team is running around and falling all over itself." Like providencejim mentioned, breaking the subject out into more detail and adding the prepositional phrase circumvents the risk of either being called out as incorrect or sounding just plain silly.

If you look at the etymology for a few of these valid words, you will find that the -cal version came from the -cally adverb form of the noun. It's just one of those linguistic evolutions that stemmed from -cally being more palatable to writers/speakers than -ckly whenever the elusive powers that be decided on the fate of these words for English.

Since this is the case, I guess you could probably say that any word that spawned from its -cally form has essentially the same meaning as the -cal form. As Warsaw Will mentioned, though, this is definitely one of those case-by-case things, simply because of words like horrifically that do exist without their -cal adjective forms. If you do a search, though, you'll find that this is one of those lines that you can cross and get away with (like dangling prepositions). There is no formal definition or acceptance to horrifical, and I would be embarrassed to use it myself, but ask Shakespeare about how scared he was to fashion new words from playing like this - he probably structured and cleaned up more gray areas like this one than we know.

In all that mess, I forgot to post on the actual question. My verdict would be,

"Not just I [the person] who thinks"

'Thinks' is modified by the implied entity - 'the person.' 'The person' comes from 'people' which is the implied group that must be assumed due to the use of the phrase 'not just.' There must be more than one if it is not just I who thinks a certain thing.

I'm new here and apologize in advance if I break any citing rules that I may not be aware of, but I love the concept of the site!

Even though it may sound stilted, as 'I' usually does when used outside of its more common usage (especially when used improperly in an objective case), it seems most would agree that 'I' is the proper pronoun here.

Normally when I'm faced with a question on pronoun usage in a gray area, I rearrange or rephrase the sentence so that it has the exact same meaning. In this case, I would think of it as, "I am not the only person who..."

As for the conjugation of think vs. thinks, since 'I' exists in the phrase, 'think' may be given some audience, but 'only person' is the one that is doing the thinking - not 'I.' I tend to lean toward rules that are similar to prepositional phrases in cases like this.

Take this example:

(1) "I am the only one in the entire group that [think/s] we should go who [am/is] of a different opinion." In this sentence, 'I' is an entity, 'only one' is an entity, and 'the entire group that [think/s] we should go' is an entity. If the sentence read,
(2) "I am the only one in entire group who [want/s] to go and [think/s] I should get more say in the matter," then 'entire group' is one entity, 'I' is one entity, and 'only one' is one entity.

The difference is slight, and I have a personal rule that the word, 'that' links ideas into one entity while 'who' does not. This is more of a spoken/felt rule than a hard rule - I'm not sure there are any in English these days.

Back to the two examples, which entity is of a different opinion? I would break it down as follows:
In (1), the entity 'only one' is the entity that 'is of a different opinion'
In (1), the entity 'entire group' is a child entity (linked together with the word, 'that') of entity 'entire group that [think/s] we should go' and it modifies think, so it would be conjugated as 'thinks.'
In (2), the entity 'entire group' does not modify 'wants,' as I would say that 'who' is breaking out of the prepositional phrase, and now 'wants' needs to step back up the stack to look for a modifying pronoun - 'only one.'
In (2), the verb 'think' would be conjugated exactly the same as 'want,' because the same entity is carrying out the action - only one.

I apologize in advance for the explanation and if it may seem subjective or if the syntax is wrong - I'm not sure how to use italics, which would greatly help explaining when using words as words.

When I refer to an entity, I use that term because classic English grammar doesn't really give me a name for what I'm trying to express, and I want a more general term (and don't want to call it a "thing"). Ambiguity would be greatly reduced if we did have hard and fast rules like "that," vs. "who," but we all know there are two sides to every argument on similar rules, so that's what this forum is for, eh?