Nasdaq "solved" that problem by including a 5x float multiplier for stocks with less than 20% of shares available to the public...

That's misleading.

Before the changes, the Nasdaq-100 index was total market cap-weighted not float-weighted. Once a company crossed 10% floated shares, the company was added to the index at full weight.

Nasdaq's new system is a hybrid of float-weighted and cap-weighted. If a company has below 33.3% float, its weighting is 3x float. Above that, it's cap weighted. This allows a gradual fade-in of the company into the index.

It's a better system than the previous one, and in Nasdaq's own words, more conservative.

For the Nasdaq-100, SpaceX at 4% float gets 3 x 4% = 12% of its market cap counted, which is $210B not $1.75T. Still <1% of the index.

Also, the multiplier is 3x, not 5x. Nasdaq proposed 5x, but after feedback, this was reduced to 3x. The new thresholds are 3x and 33%, not 5x and 20%.

https://www.nasdaq.com/newsroom/nasdaq100-index-methodology-...