The Doctor's various TARDISes

Although they mainly used one particular TARDIS, the Doctor additionally used various different TARDISes, 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 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) Later in the conflict, the War Doctor escaped Rovidia in Vassarian's TARDIS but sabotage by Heleyna caused the Battle TARDIS to fall apart. (AUDIO: The Eternity Cage, Eye of Harmony)

After finding himself in Gallifrey's past, the Eleventh Doctor was drafted into the development of Type 1 TARDISes. Befriending one, the Doctor hoped to use its fluid links to repair his own TARDIS only for the Type 1's first flight to strand them in the Void. With the aid of his other incarnations, the Doctor managed to return to N-Space, though the Type 1 chose to remain in the Void, content with the peace and quiet. (COMIC: The Lost Dimension)

When the Eleventh Doctor and Idris needed to escape House's universe, they built a makeshift TARDIS out of various TARDIS parts. This TARDIS was destroyed when the TARDIS control room it was in was deleted by House. (TV: The Doctor’s Wife)

Upon returning to Gallifrey and pulling Clara Oswald out of time via extraction chamber 7, the Twelfth Doctor stole a new TARDIS to escape. When the Doctor later lost his memories of Clara, she claimed the TARDIS for herself. (TV: Hell Bent)

The Thirteenth Doctor stole the Spy Master's TARDIS to get back to 2020 from World War II. (TV: Spyfall) The Doctor retained possession of this TARDIS after the Master became trapped in the Kasaavin realm. (PROSE: TARDIS Tour)

During the Restoration of the Cyber-Empire, the Thirteenth Doctor sent Team TARDIS home via a TARDIS. She later commandeered another to escape the detonation of the death particle. While the Doctor abandoned the second TARDIS once she reunited with her own, (TV: The Timeless Children) the first was later remotely sent to the Void to defeat an army of Death Squad Daleks. (TV: Revolution of the Daleks)