A few more "hundred" vs "hundreds"
Solution 1:
We use the singular when the magnitude number is modified by few:
We need a few hundred dollars.
We need a few thousand widgets.
If we keep the object, we would put more after the number:
We need a few hundred more dollars.
We need a few thousand more widgets.
But if we drop the explicit object and go with the "few ... more" construction, the demarcation is not so clear, because the number becomes the object in the sentence:
We need a few hundred more.
We need a few thousand more.
We need a few more hundred.
We need a few more thousand.
While it is stylistically better to use the former in writing, you hear the latter case used all the time in speech, and it is readily understood. In this case, it would be misleading (or at least ambiguous) to pluralize the numbers, because it would imply that the number is an unbreakable unit. Note that the latter still considers the number to be somewhat unitary, but not rigidly so. This is an important distinction.
If you were to say
We need a few more hundreds.
it could be construed as meaning the need was specifically for hundred-dollar bills, instead of a quantity of money that is merely in the hundreds of dollars.
But if you say
We need a few more hundred.
you are asking the listener to consider "hundred" as a softer kind of unitary grouping.
Example from real life: When I got my current job, my salary demand was slightly higher than their range allowed. I declined the offer, but the company really wanted to hire me, so after consultations with management the company representative called me back and said, "It turns out we can come up with a few more thousand after all." He might easily have said "a few thousand more," but the way he put it put more emphasis on increments of one thousand than increments of "thousands of ones." I hope I'm making this clear, because the more I write, the finer this distinction sounds, and yet I do feel it is an important usage distinction to make and understand.
Solution 2:
Maybe it would help to think of how it is used. When a cardinal number is used as an adjective, it is treated as adjective in that it does not change number. There is a red house. There are many more red houses. ... Red does not change. There is one (more) house. There are five hundred (more) houses.
OR ... think of it as a suffix like -teen or -ty. These do not change when used as numbers: There are seventeen more houses. There are sixty more houses. There are two hundred (more) houses.
The more doesn't change anything here.
When hundred is a noun then it can be made plural. A hundred-dollar bill can be shortened to a hundred. Here it is a noun: I need two more hundreds (meaning 100-dollar bills).
Then there is the one that is tripping you up ... as a predeterminer/multiplier (not sure of the exact part of speech) ... I see hundreds (of houses). I need hundreds more (meaning I need an unspecified timesing of a hundred more). BUT ... if you know the exact number then becomes an adjective again without the plural ... I need 500 (five hundred) (more) houses.
The same applies to thousand or million. I need thousands more ... I need millions more.
I don't know if that helps or makes it murkier! lol
Solution 3:
For unknown numbers, we can use "more" with the order of magnitude as in dozens more, hundreds more, and so on.
There are 12,000 Starbucks locations in the U.S., and thousands more abroad.
The national debt is over $15 trillion, but the unfunded liability for Social Security is tens of trillions more.