Sorry for posting sequentially (shopkeeper sutta, and the 6 animals sutta) instead of one large post, but here is the most technical sutta on having one object:
Suda sutta (SN 47.8) is about a foolish monk who does satipathana but does not get concentrated because he doesn’t pay attention to nimittas.
That foolish, incompetent, unskillful mendicant doesn’t get blissful meditations in this very life, nor do they get mindfulness and situational awareness.
Sa kho so, bhikkhave, bālo abyatto akusalo bhikkhu na ceva lābhī hoti diṭṭheva dhamme sukhavihārānaṃ, na lābhī satisampajaññassa.
Why is that?
Taṃ kissa hetu?
Because they don’t take their mind’s hint.
Tathā hi so, bhikkhave, bālo abyatto akusalo bhikkhu sakassa cittassa nimittaṃ na uggaṇhāti.
Now this requires research because the sutta only refers to citassa nimitta, but if you research other suttas on tranquility, you will see the abyagga nimitta and samatha nimitta arise together and lead to citassa nimitta.
And what fuels the arising of the awakening factor of immersion, or, when it has arisen, fully develops it?
Ko ca, bhikkhave, āhāro anuppannassa vā samādhisambojjhaṅgassa uppādāya, uppannassa vā samādhisambojjhaṅgassa bhāvanāya pāripūriyā?
There are things that are the foundation of serenity and freedom from distraction.
Atthi, bhikkhave, samathanimittaṃ abyagganimittaṃ.
Frequent proper attention to them
fuels the arising of the awakening factor of immersion, or, when it has arisen, fully develops it.
ayamāhāro anuppannassa vā samādhisambojjhaṅgassa uppādāya, uppannassa vā samādhisambojjhaṅgassa bhāvanāya pāripūriyā.
Abyagga means “non-distraction” aka one pointedness. If you are distracted you cannot become concentrated, and so a foolish monk does satipathana without concentration (cough vipassana cough momentary concentration)