The Doctor's various TARDISes

Although they mainly used one particular TARDIS, the Doctor additionally used various different TARDISs, both before using their usual TARDIS (PROSE: Cold Fusion, TV: Fugitive of the Judoon) and in exceptional circumstances. (PROSE: The Shadows of Avalon, AUDIO: Saviour)

Before their usual TARDIS
According to one account, the Fugitive Doctor, an incarnation prior to the First Doctor and after the Timeless Children who was active during the Dark Times (TV: Once, Upon Time), used a TARDIS with a police box exterior and a white console room. (TV: Fugitive of the Judoon)

According to another acount, Patience's husband used a prototype TARDIS before the coinage of the term, called The Machine, which caused violent ruptures in the Time Vortex. (PROSE: Cold Fusion). The description of this TARDIS's interior matched the human scientist Dr. Who's TARDIS. (TV: Dr. Who and the Daleks)

According to multiple accounts, the First Doctor owned a Type 50 TARDIS before he left Gallifrey. This TARDIS was angry that the Doctor had chosen a Type 40 when he left, calling it "inferior". (AUDIO: Prisoners of Fate). According to another account, he almost stole a faulty capsule before being redirected by an an echo of Clara Oswald. (TV: The Name of the Doctor)

During exceptional circumstances
After his usual TARDIS was destroyed by a dimensional tear, the Eighth Doctor and Fitz Kreiner travelled within the humanoid timeship Compassion, who was also their companion (PROSE: The Shadows of Avalon) until the Faction Paradox invasion of Gallifrey. (PROSE: The Ancestor Cell)

During the Last Great Time War, the War Doctor was forced by Veklin to use a Battle TARDIS in an attempt to make him more controllable. (AUDIO: Saviour)