OK, here are some comments from Bhikkhu Bodhi (BB) and Commentary (Spk).
BB: The seven cases (sattatthana) are obtained by merging the tetrad of the preceding sutta with the triad of SN 22:26.
[As we have already discussed above.]
Spk: This sutta is a statement of both congratulations (ussada-nandiya) and enticement (palobhianiya). For just as a king who has won a battle rewards and honours his victorious warriors in order to inspire the other soldiers to become heroes, so the Blessed One extols and praises the arahants in order to inspire the others to attain the fruit of arahantship.
BB: A triple investigator (tividhupaparikkhi). This may be understood by way of the Dhatusamyutta(SN 14, Elements http://awake.kiev.ua/dhamma/tipitaka/2Sutta-Pitaka/3Samyutta-Nikaya/index.html
), the Salayatanasamyutta (SN 36, The six senses http://www.accesstoinsight.org/tipitaka/sn/index.html#sn35
), and tha Nidanasamyutta (SN 12, Paticcasamuppada (dependent co-arising) http://www.accesstoinsight.org/tipitaka/sn/index.html#sn12
). See too MN 115 http://www.mahindarama.com/e-tipitaka/Majjhima-Nikaya/mn-115.htm
, where skill in the elements, sense bases and dependent origination is explained in detail, augmented by the skill of knowing the possible and the impossible.