Does this stand have multiple positions at which the height can be set, or is it a "fully up or fully down" sort of thing?

This is fully adjustable (infinite).

Questions & Answers: Rosewill RMS-19044 Height Adjustable Standing Desk Riser Monitor Stand, 29-Inch Pre-Assembled Slim Portable Sturdy Desktop Computer Laptop Stand, Ergonomic Sit to Stand Office Workstation

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Rosewill RMS-19044 Height Adjustable Standing Desk Riser Monitor Stand, 29-Inch Pre-Assembled Slim Portable Sturdy Desktop Computer Laptop Stand, Ergonomic Sit to Stand Office Workstation

Adjustable Ergonomic Sit to Stand Desk: Set your desired height with one smooth, stepless motion from 1.80 to 16.10 inches; quickly transition from a sitting to standing desk with little effort; change up your work habits and experience ergonomic comfort
Spacious Workstation: Large desktop surface measures 29.30 x 17.70 inches to fit multiple screens, including a dual monitor setup or one monitor plus laptop, with plenty of room for a keyboard and mouse; sturdy steel frame supports up to 22 pounds maximum
Completely Pre-Assembled: Comes ready to use right out of the box with no assembly needed; slim design, portable and easy to store

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