Fundamentally what has always excited me about jamming has not been making music that necessarily sounds good (although that's nice too) but instead creating musical experiences that are novel.

Jams tend to happen with a jazz, rock, or blues context, but my preference is to generally avoid this tradition. When genre is invoked people will inevitably rely upon stylistic clichés, making it harder to arrive at some new experience. In addition, these genre-based jams end up manifesting as trading solos back and forth over the same chord or a simple progression for 30 minutes straight. It's very one-dimensional.

Removing the context of genres does take away structure. So in that absence I propose other structural ideas for jamming.

These ideas are formulated with two people in mind, but they can be adjusted to accomodate more people.

Person 1 plays a note. Person 2 plays a note. Person 1 plays a note. Etc.

Try to complete each other's musical thoughts or make it sound like one person is playing.

Try to compliment each other's thoughts. Maybe one person plays bass notes and the other plays higher notes. This becomes easier when you alternate 2 or 3 notes at a time instead. Try to make it sound like a Bach invention.

Try to evolve the melody to different keys.

Pick a chord, close eyes, and try to play in sync with no tempo. Leave lots of space in between.

Try altering the chord after some time. Do something simple like add a 7th or change to another chord that might superimpose well with the original chord. But mostly focus on playing and releasing together.

Take a song both people have never heard. Use source separation to strip away everything but the voice. Play the vocal track and try to come up with an accompaniment that makes sense. If it's too difficult, maybe add just the drums or bass. If it's still too difficult, add in other instruments. After coming up with something, compare it to the full mix.

Take a song both people have never heard. Use source separation to strip away the drums. Have one person command the bass+snare drum while the other person takes care of everything else. Try to come up with a drum part and play it together. Experiment with each person taking different pieces of the kit.

Pick a song where Person 1 knows a song that Person 2 is unfamiliar with. Without playing the song, Person 1 will write out the sections of the song in very vague details (Verse: "Rhythmic Bb and Eb major figure", Chorus: "A moderate moving chord progression around G minor", etc.). Person 1 will extract just the drum part and play it for Person 2 while Person 2 comes up with parts each of the sections that Person 1 described. They then learn this new derivative song together.

Not improvisation, but still can be fun, refreshing, and exploratory -- just sight read music together.