There have been a couple types of slide saxes made but for whatever reason they haven't really caught on..
This one has keys that are actuated by the slide:
https://www.youtube.com/watch?v=NJU9Rm-KviI
(The last third of the video has a narrative in French describing the instrument, photobombed by a set of four serpents hanging on the wall behind the speaker. A serpent is a instrument that is sort of the opposite of a slide sax: it combines a brass-style mouthpiece with woodwind-like fingerholes).
This one has keys that are actuated by the slide: https://www.youtube.com/watch?v=NJU9Rm-KviI (The last third of the video has a narrative in French describing the instrument, photobombed by a set of four serpents hanging on the wall behind the speaker. A serpent is a instrument that is sort of the opposite of a slide sax: it combines a brass-style mouthpiece with woodwind-like fingerholes).
This one looks mechanically simpler but it's not conical bore like a real saxophone: https://www.youtube.com/watch?v=vjnrM3GZMS8