A place where there is a similar usage to Matthew 21:34 with λαμβάνειν + an accusative of what belongs or should be given to somebody is
Matthew 15:26 wrote: Ὁ δὲ ἀποκριθεὶς εἶπεν, Οὐκ ἔστιν καλὸν λαβεῖν τὸν ἄρτον τῶν τέκνων, καὶ βαλεῖν τοῖς κυναρίοις.
In the synoptic parallels to Matthew 21:34,
Mark 12:2 wrote:Καὶ ἀπέστειλεν πρὸς τοὺς γεωργοὺς τῷ καιρῷ δοῦλον, ἵνα παρὰ τῶν γεωργῶν λάβῃ ἀπὸ τοῦ καρποῦ τοῦ ἀμπελῶνος.
Luke 21:10 wrote:καὶ ἐν καιρῷ ἀπέστειλεν πρὸς τοὺς γεωργοὺς δοῦλον, ἵνα ἀπὸ τοῦ καρποῦ τοῦ ἀμπελῶνος δῶσιν αὐτῷ· οἱ δὲ γεωργοὶ δείραντες αὐτὸν ἐξαπέστειλαν κενόν.
The partative genitive with ἀπὸ is used of the produce, and instead of the αὐτοῦ that is to be found in Matthew 21:34, those two Evangelists make clear the referent, by using τοῦ ἀμπελῶνος. If supposing or hypothesis ingredients is thinking outside the box to better understand what is in the box, then it is worthwhile to ask, "What if the ἀπὸ τοῦ καρποῦ τοῦ ἀμπελῶνος had been ἀπὸ τοῦ καρποῦ αὐτοῦ?". The ἀπό is still ἀπό, because they were sent to remove some of the produce from the context of the vineyard and take it for sale or for their master's use.
With the corresponding (complementarily antonymous) verb δίδωμι Matthew 25:8 is used in a context of a request, which could be trying to formally a contrast between their situation and that of the others:
Αἱ δὲ μωραὶ ταῖς φρονίμοις εἶπον, Δότε ἡμῖν ἐκ τοῦ ἐλαίου ὑμῶν, ὅτι αἱ λαμπάδες ἡμῶν σβέννυνται.
Perhaps something like, "C'mon, you're not going to miss it. Just a little.". It seems that the imprudent young women are portrayed as using some form of exageration to get their point across. The prudent young women reply by expressing a fear, which may be a more realistic evaluation of the situation, which is that they will need more than the little bit of their oil ἐκ τοῦ ἐλαίου ὑμῶν that will be needed to keep the lamps from going out.
Luke 15:16 wrote:Καὶ ἐπεθύμει γεμίσαι τὴν κοιλίαν αὐτοῦ ἀπὸ τῶν κερατίων ὧν ἤσθιον οἱ χοῖροι· καὶ οὐδεὶς ἐδίδου αὐτῷ [γεμίσαι τὴν κοιλίαν αὐτοῦ ἀπὸ τῶν κερατίων ...].
In terms of the partitive genitive in Luke and Mark then, there may be an intended pathos, contrasting (the seriousness of) the killing with the (small or expected) amount of the produce that were going to give. If somebody had come and demanded the food out of their children's mouths, then maltreating the servants might not seem so pointless or tragic. In Matthew it is probably a contrast between rightful or legal (contractual) amount of the fruit due to the owner, and the mistreatment.
In case anyone is wondering, the prodigal son uses the more formal language (of a system of calculating - either legal or economic):
Luke 15:12 wrote:καὶ εἶπεν ὁ νεώτερος αὐτῶν τῷ πατρί, Πάτερ, δός μοι τὸ ἐπιβάλλον μέρος τῆς οὐσίας. Καὶ διεῖλεν αὐτοῖς τὸν βίον.