Can a player choose to mulligan to zero cards in Commander?

In Commander, the mulligan rule follows the Vancouver/London mulligan system used in official formats. Under CR 103.4, each player may take any number of mulligans, each time shuffling their hand into their library and drawing a new hand of seven cards. After all mulligans are taken, each player who took one or more mulligans puts cards from their hand on the bottom of their library equal to the number of times they mulliganed.

Crucially, CR 103.4 does not set a minimum on how many times you can mulligan — you may keep mulliganing until you choose to keep. Since you can always choose to mulligan again rather than keep, you could theoretically mulligan six times (drawing a hand of seven each time, then putting six cards on the bottom), ending with one card, and then mulligan once more to end with zero cards in hand after putting one card on the bottom.

Commander's specific rules (as established by the format's rules committee) do not override or restrict this. The format uses the same London mulligan procedure. There is no rule preventing a player from keeping a hand of zero cards, strange as it may be.

Concrete example: Alice is playing Commander and has an extremely unlucky run. She mulligans six times, each time drawing seven and putting more cards back. On her seventh drawn hand, she decides to mulligan again — she shuffles in, draws seven, then must put seven cards on the bottom, leaving her with zero cards. She declares she keeps. Her turn begins with zero cards in hand and no draw in her first turn (as the first player skips their draw step per CR 103.7a).

This is referenced under CR 103.4 and 103.4b (the London mulligan rule). There is no Commander-specific rule (CR 903) that prevents mulliganing to zero. It is legal, though almost certainly a concession in practice.