From looking at the mechanics of Body Thief I can't see why not, but I may be missing something.
The intellect devourer initiates an Intelligence contest with an incapacitated humanoid [...] If it wins the contest, the intellect devourer magically consumes the target's brain, teleports into the target's skull, and takes control of the target's body. (Monster Manual, p.191)
I just want to know whether this could be possible.
The intellect devourer initiates an Intelligence contest with an incapacitated humanoid...
The Intellect Devourer does not change its creature type by consuming a brain and taking over its body. Since the Intellect Devourer itself isn't Humanoid, the taken-over creature's body is not a valid target for Body Thief. It is and will always be:
Intellect Devourer
Tiny aberration, lawful evil
In fact, the body is acting pretty much like a "mech" for the tiny creature, as it hides in the skull cavity. It's not a creature, it's... a puppet of sorts - the Intellect Devourer uses the body, and discards it when damaged too much, or it wants to disembarks.
While inside a creature, the intellect devourer has total cover against attacks and other effects originating outside its host.
The Body Thief ability states
The intellect devourer initiates an Intelligence contest with an incapacitated humanoid within 5 feet of it that isn't protected by protection from evil and good. If it wins the contest, the intellect devourer magically consumes the target's brain, teleports into the target's skull, and takes control of the target's body. While inside a creature, the intellect devourer has total cover against attacks and other effects originating outside its host. The intellect devourer retains its Intelligence, Wisdom, and Charisma scores, as well as its understanding of Deep Speech, its telepathy, and its traits. It otherwise adopts the target's statistics. It knows everything the creature knew, including spells and languages.
(emphasis mine)
From this, i would infer, that the original humanoid does not exist anymore, i.e. the (once humanoid) creature's body with an intellect devourer in place of its lost brain is no longer a humanoid and therefore no longer a valid target for the Body Thief ability.
There is no rule that directly specifies this as far as I'm aware so every DM would have to decide this for themselves but I don't think this should be possible.
First off, the trait specifies that it only works on a humanoid, it's debatable whether a body with an intellect devourer inside it still counts as a humanoid but I would say it doesn't anymore, it's just a meatsuit for the intellect devourer.
IIRC, 3.5E entry on intellect devourers specified that once inside a host it "animates the body", suggesting that it's just that, a body, not a creature anymore, 5E no longer says it but I think that was quite descriptive of the intent. Still, the 5E description of Body Thief refers to a host with an intellect devourer inside as either "host body" or just "body", not a creature. So I would say from this alone that it already doesn't work.
Going further, the trait states:
(…) If it wins the contest, the intellect devourer magically consumes the target's brain (…)
So the target must have a brain for this to work, not another devourer inside its skull. That's another strike I would count against.
Overall I would just say that this is not going to work as there is no valid target to use the feature on.
The most another intellect devourer could do would be to keep attacking the body until it drops to 0hp, forcing the one inside it to come out but that still just leaves you with a dead body on the ground, with empty space inside its skull after 1 round, not a target. It would maybe give the devourer a short window of opportunity during that single round with the body at 0hp but not yet dead as RAW it would count as unconscious but that would also be up to the DM and is also debatable. And unless it had some way of healing the body back up, it would also end up expelled immediately after and the body would end up dead.
The description of the action leaves some possible ways to decide in a way or another: at the end, it is a DM call.
The target must be
[...] an incapacitated humanoid within 5 feet of it that isn’t protected by protection from evil and good.
Is a creature with an Intellect Devourer (ID) (inside the skull) a suitable target, once it is incapacitated, within 5 feet and without the protection of the mentioned spell? Yes, since it is an humanoid (emphasis mine):
The intellect devourer retains its Intelligence, Wisdom, and Charisma scores, as well as its understanding of Deep Speech, its telepathy, and its traits. It otherwise adopts the target’s statistics.
The target's statistics encompass also the type: hence, the Mind Thief action can be used against a creature with an ID inside.
Anyway, another problem emerges: can ID in the humanoid "form" be targeted another Devourer's Mind Thief ? Indeed, the description of Mind thief says:
While inside a creature, the intellect devourer has total cover against attacks and other effects originating outside its host.
Here there are two possible interpretation:
The actual target of Mind Thief is the creature, not the brain or the skull's interiors of the creature: but an ID-controlled creature is an ID which has total cover from effects per description.
The DM has to make a call in this case.
The description says:
If it wins the contest, the intellect devourer magically consumes the target’s brain, teleports into the target’s skull, and takes control of the target’s body. [...] It knows everything the creature knew, including spells and languages.
Hence, the target's brain is no more and the ID takes its place, functioning as the brain but without being a brain.
Again, there is a little bit of room for interpretation: a DM could rule that an ID can challenge the ID inside a creature, considering the latter as an actual brain, for taking control of the body1.
Recalling that the description is part of the monster statistics, one can read:
Deadly Puppet Masters. An intellect devourer consumes a creature’s mind and memories, then turns the host body into a puppet under its control. An intellect devourer typically uses its puppet host to lure others into the domain of the mind flayers to be enthralled or consumed.
Hence, typically an ID serves its Illithid masters and uses its Mind Thief to convince other victims into Mind Flayers hands/tentacles: two IDs have little motivation to battle for one body.
Of course, the key is the word "typically": there may be some outliers in the ID population that may act in different ways.
1 I like to think to this case as hermit crabs fighting for a shell...
