How do Mahayana doctrines make sense of arahants can come back to become Buddhas, with no self?

When the arahant dies and has no further mind or body arising again, there's no way to point to anything and say that's the individual arahant. Or else we are pointing to a soul, a self.

There is a distinction between mind and unfabricated mind.

The first of the eleven topics, arguably the most important, deals with the generic basis, which is initially defined by Vimalamitra in the section on the nidāna as “one’s unfabricated mind” (rang sems ma bcos pa).

This crucial point should not be overlooked, for it would appear that Vimalamitra’s stance contradicts the modern tendency to interpret the generic basis as a transpersonal entity of some kind.

Smith, Malcolm. Buddhahood in This Life: The Great Commentaryby Vimalamitra (pp. 14-15). Wisdom Publications. Kindle Edition.

Tantras are very important in the Mahayana abhidharma systems. Tantras are not things themselves but connections between things.

“Tantras” are tantras because of connection, and further, because they connect the basis, the method, and the result. When divided, there are two kinds: tantras of words and tantras of meaning. Words are sounds. There are three in the tantras of meaning: the tantra of the basis, the tantra of the method, and the tantra of the result. Now then, the tantra of the basis is the nature of the two truths, the method is the two stages, and the result is the two kāyas, the dharmakāya and the rūpakāya. Therefore, since the result is obtained when the method is cultivated in dependence on the basis, a tantra is so called because it connects. Vimalamitra uses the three tantras to map the eleven topics in the following way: the first seven topics correspond to the basis. Within these, the first and second deal with the generic basis (spyi gzhi), while topics 3 through 7 describe the person as the basis in terms of defining human anatomy from the perspective of the intimate instruction class of the Great Perfection. Topics 8 through 10 set forth the path. Finally, the eleventh topic defines the result.

Smith, Malcolm. Buddhahood in This Life: The Great Commentary by Vimalamitra (p. 14). Wisdom Publications. Kindle Edition. In Mahayana the ‘tantra of the basis’ is the root of the 2 truths…. the dharmakāya and the rūpakāya.

This represents a what is called process metaphysics vs substance metaphysics. Dogens view that all things are time not things…being-time. Substance metaphysics vs Process metaphysics or why I don't consider myself a materialist/physicalist : zenbuddhism (reddit.com) So we are not pointing to a self/soul but to a process arising from connections made while existing as a phenomenological manifestation of being-time during this life. The “thermodynamics” created within the rūpakāya give rise to other states of being that are not self or soul but a particular karmic configuration of connections.

/r/Buddhism Thread