How exactly does the Dispel Magic spell work against higher-level spells?

There has been a lot of debate in my D&D group about the specific wording of Dispel Magic which were not answered by the D&D Sage Advice Compendium:

Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends. For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell’s level. On a successful check, the spell ends.

How many rolls does one have to make in order to break a 9th-level spell with a 3rd-level spell slot?

The primary issue revolves around the interpretation of the word “any” here. In English the word “any” could mean “any one” or “any of your choice”.

I have seen a couple of forum posts suggesting that if three mages each cast Haste on a single target, and you use Dispel Magic on that target, then it will only remove one instance of Haste.

If we agree with this “only one effect can be removed” definition, then it leads to different interpretation of the next sentence:

“For each spell level higher on the target, make an ability check”

If this is the case, then removing a 9th-level spell using a 3rd-level slot would require 6 rolls:

  1. A DC 14 to break the 4th level
  2. A DC 15 to break the 5th level
  3. A DC 16 to break the 6th level
  4. A DC 17 to break the 7th level
  5. A DC 18 to break the 8th level
  6. A DC 19 to break the 9th level

On the one hand, this sounds almost reasonable. If you only need to make a single ability check to remove a 9th-level world-altering magical effect with a 3rd-level spell slot, then a level 5 wizard could by pure luck banish an eldritch god to the outer planes. This seems extremely powerful and beyond the scope of a 5th-level character.

On the other hand, if this really is how Dispel Magic works, then the odds of dispelling a 9th-level spell with a 3rd-level slot for a character with 20 Intelligence is only 1%. Even using a 6th level slot to improve your odds only gets you up to 6.3%.

If, on the other hand, it only takes a single roll to remove a 9th-level spell – then I have a related question regarding the wording “for each spell” which can be seen here: How exactly does the Dispel Magic spell work with multiple effects?