And here's the solution. It's also doable with two people if one of them is very good at jumping.
[sblock]
Step 1. You have four PCs (Al, Barb, Cat, and Dan). Al taps the blue stone. The blue bridges go up, and the orange walls go down. Barb goes across the southeast blue bridge.
Walls up--: RYGBV
Bridges up: B
Step 2. Al taps the orange stone. The blue bridge and walls vanish, and the orange walls and bridges appear. Cat and Dan goes across the southwest orange bridge, and Barb goes up to the eastern platform.
Walls up--: ROYGV
Bridges up: O
Step 3. Al taps blue again. This lets Cat and Dan go up to the western platform, and lets Barb reach the red stone.
Walls up--: RYGBV
Bridges up: B
Step 4. Barb taps the red stone, then backs out so she doesn't get trapped. Cat goes up to the northwest platform and waits in front of the red wall.
Walls up--: RYBV
Bridges up: RB
Step 5. Al taps the orange stone and then Dans tap the green stone. Barb goes up to the northeast platform and waits in front of the violet wall.
Walls up--: OYGV
Bridges up: OG
Step 6. Cat taps the yellow stone.
Walls up--: OYG
Bridges up: OYG
Step 7. Dan walks across the yellow bridge to the red stone. He taps it, and then moves back to the middle of the bridge. Cat comes back to the western platform.
Walls up--: ROY
Bridges up: ROY
Step 8. Barb taps the violet stone. The yellow bridge vanishes but the violet bridge appears right beneath Dan, so he doesn’t fall.
Walls up--: ROV
Bridges up: ROV
Step 9. Cat taps green. Dan walks onto the north platform, and is now past the red veil. Barb walks down to the east platform.
Walls up--: OGV
Bridges up: OGV
Step 10. Al taps blue. Dan walks past the orange veil and yellow veil, and Barb moves beside the red stone.
Walls up--: GBV
Bridges up: GBV
Step 11. Barb taps the red stone and Al taps the orange stone. Dan walks past the green and blue veils.
Walls up--: ROV
Bridges up: ROV
Step 12. Al toggles blue and orange so Barb can walk from east, to southeast, to south, to southwest, to west, to northwest. Then Cat taps green so Barb can tap yellow, dropping the final veil. Dan taps the white stone.
Walls up--: None.
Bridges up: All.
[/sblock]