In oral study system (reciting and memorizing)...
I definitely sure according to Mahasatipatthanasutta's structure "aparam" means "next step". For an example, after the practitioner meditated the previous body (breath) in (entire) body (in sitting posture), next step when the practitioner is going, he is clearly understanding "I am walking (with clearly understanding in breath, 32 organs, 4 elements, etc.)" In the blanket is omitted as understood from the previous Pabba in oral study tradition.
Niddharana (list) is the meaning of the sattamii vibhatti of kaaye (entire body), kaayaanupassi and kaayasmim (body's part), vedanaasu, citte, cittasmim, dhammesu.
"Puna ca" means another Pabba.
Vasi (practice to be professional) is objective of internal, external, internal&external, iriyaapathapabba, and sampajaanapabba which next step from sitting-iriyaapatha in aanapanapabba (and other Pabba).
So, I am not sure of "and further", "again" meaning in all translations. According to each Sutta's context and history, MahasatipatthanaSutta is for no-unawesome-mind-practitioner or attained jhana practitioner (vipassanayaanika), and KaayagatasatiSutta is for newbie jhana practitioner (samathayaanika) and Anapanassati is samatha, so I quoted from KaayagatasatiSutta...
[294] Kathaṃ bhāvitā ca bhikkhave kāyagatā sati kathaṃ bahulīkatā mahapphalā hoti mahānisaṃsā . idha bhikkhave bhikkhu araññagato vā rukkhamūlagato vā suññāgāragato vā nisīdati pallaṅkaṃ ābhujitvā ujuṃ kāyaṃ paṇidhāya parimukhaṃ satiṃ upaṭṭhapetvā . so satova assasati sato passasati . dīghaṃ vā assasanto dīghaṃ assasāmīti pajānāti dīghaṃ vā passasanto dīghaṃ passasāmīti pajānāti . Rassaṃ vā assasanto rassaṃ assasāmīti pajānāti rassaṃ vā passasanto rassaṃ passasāmīti pajānāti . sabbakāyapaṭisaṃvedī assasissāmīti sikkhati sabbakāyapaṭisaṃvedī passasissāmīti sikkhati . Passambhayaṃ kāyasaṅkhāraṃ assasissāmīti sikkhati passambhayaṃ kāyasaṅkhāraṃ passasissāmīti sikkhati . tassa evaṃ appamattassa ātāpino pahitattassa viharato ye gehasitā sarasaṅkappā te pahīyanti . Tesaṃ pahānā ajjhattameva cittaṃ santiṭṭhati sannisīdati ekodibhoti 1- samādhiyati evampi bhikkhave bhikkhu kāyagataṃ satiṃ bhāveti.
[295] Puna caparaṃ bhikkhave bhikkhu gacchanto vā gacchāmīti pajānāti ṭhito vā ṭhitomhīti pajānāti nisinno vā nisinnomhīti pajānāti sayāno vā sayānomhīti pajānāti . yathā yathā vā panassa kāyo paṇihito hoti tathā tathā naṃ pajānāti . Tassa evaṃ appamattassa ātāpino pahitattassa viharato ye gehasitā sarasaṅkappā te pahīyanti . tesaṃ pahānā ajjhattameva Cittaṃ santiṭṭhati sannisīdati ekodibhoti samādhiyati evampi bhikkhave bhikkhu kāyagataṃ satiṃ bhāveti.
@Footnote: 1 Ma. Yu. ekodi hoti.
Thaanissaro translation...
"There is the case where a monk — having gone to the wilderness, to the shade of a tree, or to an empty building — sits down folding his legs crosswise, holding his body erect and setting mindfulness to the fore. Always mindful, he breathes in; mindful he breathes out.
"Breathing in long, he discerns, 'I am breathing in long'; or breathing out long, he discerns, 'I am breathing out long.' Or breathing in short, he discerns, 'I am breathing in short'; or breathing out short, he discerns, 'I am breathing out short.' He trains himself, 'I will breathe in sensitive to the entire body.' He trains himself, 'I will breathe out sensitive to the entire body.' He trains himself, 'I will breathe in calming bodily fabrication.' He trains himself, 'I will breathe out calming bodily fabrication.' And as he remains thus heedful, ardent, & resolute, any memories & resolves related to the household life are abandoned, and with their abandoning his mind gathers & settles inwardly, grows unified & centered. This is how a monk develops mindfulness immersed in the body.
"''Furthermore'', when walking, the monk discerns, 'I am walking.' When standing, he discerns, 'I am standing.' When sitting, he discerns, 'I am sitting.' When lying down, he discerns, 'I am lying down.' Or however his body is disposed, that is how he discerns it. And as he remains thus heedful, ardent, & resolute, any memories & resolves related to the household life are abandoned, and with their abandoning his mind gathers & settles inwardly, grows unified & centered. This is how a monk develops mindfulness immersed in the body.
Do "and further", "again", surely mean "next step"?