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In the new sourcebook Mythic Odysseys of Theros, the Satyr gains the ability Mirthful Leaps:

Whenever you make a long or high jump, you can roll a d8 and add the number rolled to the number of feet you cover, even when making a standing jump. This extra distance costs movement as normal.

If you have a multiplier on jump distance, such as that provided by the Boots of Striding and Springing...

In addition, you can jump three times the normal distance, though you can't jump farther than your remaining movement would allow.

... would the +1d8 feet be multiplied by three as well?

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I would make the argument that when Boots of Striding and Springing says

you can jump three times the normal distance,

this is referring to your unmodified (normal) jump distance, to which you may then add modifiers.

I believe if the Boots multiplied the modifiers as well, it would read similar to the Jump spell:

the creature's jump distance is tripled

Jump triples your jump distance for its duration, modifiers included; if it was intended to triple your distance without first accounting for modifiers it would read as the Boots do, using the word "normal".

Thanks to Medix2 for helping with clarity.

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    \$\begingroup\$ Thanks again @Medix2, this is my first time answering a question here. \$\endgroup\$ – Thomas Markov Jun 4 at 15:03
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    \$\begingroup\$ You're totally good, and this honestly pointed out something I certainly would have missed; great first answer! \$\endgroup\$ – Medix2 Jun 4 at 15:07

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