ὅθεν ὤφειλεν κατὰ πάντα τοῖς ἀδελφοῖς ὁμοιωθῆναι, ἵνα ἐλεήμων γένηται καὶ πιστὸς ἀρχιερεὺς τὰ πρὸς τὸν θεόν, εἰς τὸ ἱλάσκεσθαι τὰς ἁμαρτίας τοῦ λαοῦ (Heb 2:17 WH)
It's possible by just considering the morphology alone that πάντα above is the accusative masc sing form of πᾶς or it could be the nominative, vocative or accusative neuter pl form, if we just think about morphology apart from context. But it is clearly acc neut pl in Heb 2:17. Furthermore, κατὰ + πάντα no doubt functions adverbially here. Note, for instance, how the writer of Hebrews employs κατὰ + πάντα in Heb 4:15.
πᾶς is simply the lexical form of πάντα and it also functions vocatively in some contexts/uses (masc sing) although not in 2:17.
I will appeal to Zerwick's Grammatical Analysis for the verb ὤφειλεν and the construction κατὰ πάντα:
"ὤφειλεν he had to, impf ὀφείλω owe; w. inf. ought. κατὰ πάντα in all respects, in everything."
As we learn from what is written above, Christ became like his brothers/sisters in all respects since τοῖς ἀδελφοῖς is pl dative and ὤφειλεν means "he was owing" or "he had to" or "it behooved him" (KJV). Moreover, ὁμοιωθῆναι (aorist infinitive passive) should be construed with τοῖς ἀδελφοῖς. Compare Acts 14:11.
Zerwick has the following:
"ἐπιλαμβάνομαι τίνος take [something] upon oneself (mid.), take on, as in Eng. [with] connotation of responsibility for" (p. 658).
Here is also the most pertinent part of what BDAG has to say about ἐπιλαμβάνομαι, but I encourage our blog readers (if it is possible) to read the complete entry for this verb:
"be concerned with/about. The context of ἀγγέλων, σπέρματος Ἀβραὰμ Heb 2:16 suggests the rendering take an interest in, prob. in the sense *help* (schol. on Aeschyl., Pers. 742 [but s. KDolfe, ZNW 84 '93, on the textual problem]; Sir 4:11)."
ἐπιλαμβάνομαι can mean, "to make the motion of grasping or taking hold of [something], take hold of, grasp, catch," but that is not necessarily its sense in Heb 2:16. It is imperative to understand how an author employs a word in a determinate context since linguistic symbols usually have numerous potential meanings. Usus loquendi (usage in context) thus plays a formative linguistic role.
So κατὰ + πάντα is functioning adverbially in Heb 2:17, "in all respects" or "in every respect." Additionally, it seems that Jesus was fully human (like his brothers/sisters) and not fully God (also like his adelphoi).