How many past lives can an arahant recall?

Only the 6th one, destruction of āsavas, is exclusive to the buddhist arahants. The other five can be done with anyone with a high enough quality 4th jhana. One of these days I might share the story about the Chinese medicine doctor who did some work on my grandfather, that doctor learned from a Taoist immortal who could emanate mind made bodies like the iddhi (power) described here:

SN 51.17 bodhi trans.

  1. Ascetics and Brahmins (2)

1“Bhikkhus, whatever ascetics or brahmins in the past wielded the various kinds of spiritual power, such that: having been one, they became many … they exercised mastery with the body as far as the brahmā world—all did so because they had developed and cultivated the four bases for spiritual power.

2“Whatever ascetics or brahmins in the future will wield the various kinds of spiritual power, such that: having been one, they will become many … [275] … they will exercise mastery with the body as far as the brahmā world—all will do so because they will have developed and cultivated the four bases for spiritual power.

3“Whatever ascetics or brahmins at present wield the various kinds of spiritual power, such that: having been one, they become many … they exercise mastery with the body as far as the brahmā world—all do so because they have developed and cultivated the four bases for spiritual power.

4“What four? Here, bhikkhus, a bhikkhu develops the basis for spiritual power that possesses concentration due to desire and volitional formations of striving. He develops the basis for spiritual power that possesses concentration due to energy … concentration due to mind … concentration due to investigation and volitional formations of striving.

5“Bhikkhus, whatever ascetics or brahmins in the past … in the future … at present wield the various kinds of spiritual power … all do so because they have developed and cultivated these four bases for spiritual power.”

See SN 51.11 or AN 5.28 for a standard descriptions of the 6 abhiñña.
The first one is considerably more difficult to do than the other 4 mundane abhiñña (mind reading, divine eye, past life recolleciton etc). So if SN 51.17 shows other ascetics and brhamins can do that one, they can definitely do the 4 “easier” ones.

This excerpt shows the case of arahants who can’t do the arūpa samadhis and not the first 5 abhiñña:

SN 12.70 liberated by wisdom

some monks declare arahantship, susima asks them if they have 5 abhinna, arupa samadhi, they say no.

:diamonds: “api pana tumhe āyasmanto evaṃ jānantā evaṃ passantā ye te santā vimokkhā atikkamma rūpe āruppā, te kāyena phusitvā viharathā”ti?
“Then knowing and seeing thus, do you venerable ones dwell in those peaceful deliverances that transcend forms, the formless attainments, having touched them with the body?”208
“no hetaṃ, āvuso”.
“No, friend.”
:diamonds: “ettha dāni āyasmanto idañca veyyākaraṇaṃ imesañca dhammānaṃ asamāpatti; idaṃ no, āvuso, kathan”ti?
21“Here now, venerable ones: this answer and the nonattainment of those states, how could this be, friends?”209 “”
“paññāvimuttā kho mayaṃ, āvuso susimā”ti.
22“We are liberated by wisdom, friend Susı̄ma.”210

So when start putting together pieces of evidence together, if an arahant can be an arhaant without any past life recollection, and non buddhist meditators can recollect many past lives, it becomes clear the recollection of past lives is dependent on 4th jhana quality, not anything intrinsically buddhist.

B.Bodhi translates aryiya-savako as “noble disciple”, implying an ariya with stream entry or higher attainment. Thanissaro in most cases I’ve seen, translates it as “disciple of the noble ones”, except maybe in contexts where it must be an ariya. I’ll be interested to see how Bhante @Sujato translates that. I prefer “disciple of the noble ones”, because it makes it more relevant for everyone. Otherwise, people tend to be complacent responsibility shirkers who think, “oh I don’t have to follow that teaching, that’s only for ariyas”.