In a multiplayer game if you gain control of another player's commander can they move it to the command zone?

In Commander, the command zone replacement effect is tied to the owner of the commander, not the current controller. Whenever a commander would be put into any zone other than the command zone (graveyard, exile, hand, library), its owner may choose to move it to the command zone instead. This is defined in the Commander rules (analogous to CR 903.9).

So if you steal an opponent's commander — via Gilded Drake, Control Magic, or a similar effect — you now control it, but you do not own it. The original owner retains the right to send it to the command zone whenever it would change zones to a non-command zone.

Importantly, this applies even while you control it. If the stolen commander would die, be exiled, be bounced to hand, or be shuffled into a library, its owner can replace that move with a move to the command zone — effectively rescuing it from your control entirely.

Example: You cast Bribery and put your opponent's Atraxa into play under your control. Later it's destroyed. Your opponent (Atraxa's owner) immediately opts to move Atraxa to the command zone instead of the graveyard — it leaves your control and is now safely in their command zone ready to be recast.

Note: While the commander is on the battlefield under your control, your opponent cannot simply move it to the command zone at will — the replacement effect only triggers when it would move to another zone due to a game event (dying, exile, bounce, etc.). They cannot activate it as a free escape from your control during normal gameplay.