Does Nikayas decribe the development and cultivation after Nibbāna?(SN 22.122)

“But, friend Sariputta, what are the things that a bhikkhu who is an arahant should carefully attend to?”
“Friend Kotthita, a bhikkhu who is an arahant should carefully attend to these five aggregates subject to clinging as impermanent, as suffering, as a disease, as a tumour, as a dart, as misery, as an affliction, as alien, as disintegrating, as empty, as nonself. For the arahant, friend, there is nothing further that has to be done and no repetition of what he has already done. However, when these things are developed and cultivated, they lead to a pleasant dwelling in this very life and to mindfulness and clear comprehension.”

Buddha saying the Arahant can however create a pleasant dwelling, by developing and cultivation.

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“An arahant should attend in an appropriate way to these five clinging-aggregates as inconstant, stressful, a disease, a cancer, an arrow, painful, an affliction, alien, a dissolution, an emptiness, not-self. Although, for an arahant, there is nothing further to do, and nothing to add to what has been done, still these things — when developed & pursued — lead both to a pleasant abiding in the here-&-now and to mindfulness & alertness.”—SN 22.122

‘Development’ of the ‘establishing’ of mindfulness refers to the refrain repeated over a dozen times in the Satipatthana sutta (DN 22, MN 10), and which is divided into three levels:

“ (1) In this way he remains focused internally on the body in & of itself, or externally on the body in & of itself, or both internally & externally on the body in & of itself. (2) Or he remains focused on the phenomenon of origination with regard to the body, on the phenomenon of passing away with regard to the body, or on the phenomenon of origination & passing away with regard to the body. (3) Or his mindfulness that ‘There is a body’ is maintained to the extent of knowledge & remembrance. And he remains independent, unsustained by [not clinging to] anything in the world. This is how a monk remains focused on the body in & of itself."

(1) is the establishing of mindfulness . (2) & (3) are development, and (2) introduces knowledge of impermanence, which would be the stage most applicable generally, including to western lay practitioners, that’s why it is focussed on here by the Buddha:

"I will teach you the frames of reference, their development, and the path of practice leading to their development. Listen & pay close attention. I will speak.

"Now, what are the frames of reference? There is the case where a monk remains focused on the body in & of itself — ardent, alert, & mindful — putting aside greed & distress with reference to the world. He remains focused on feelings in & of themselves… mind in & of itself… mental qualities in & of themselves — ardent, alert, & mindful — putting aside greed & distress with reference to the world.

"This is called the frames of reference.

"And what is the development of the frames of reference? There is the case where a monk remains focused on the phenomenon of origination with regard to the body, remains focused on the phenomenon of passing away with regard to the body, remains focused on the phenomenon of origination & passing away with regard to the body — ardent, alert, & mindful — putting aside greed & distress with reference to the world. "—SN 47.40

The third level applies to arahants. There the adept has become independent, not sustained by anything in the world.

Thank you. My friend. It’s possible that most is perception training and because of that things can be cultivated even further in jhana for example ? For them to be more stronger. Any reference to this idea in suttas to be done after Arahantship? Because as everything is changeble I assume Jhanas can become deeper.