Remove limit of 8 devices on WiFi network on Raspberry Pi?

I'm currently trying to set up a WiFi access point for ~20 students on my Raspberry Pi 3B+.
The traffic already gets properly forwarded to the other network, which is connected via the LAN port. The DHCP server (The devices don't have their own IPs in the outer network, and the Pi routes it to the outer network through the firewall) also works.
However, I've run into some issues on the wireless configuration side. The number of devices seems to be capped at 8 devices. I've already tried multiple different modes on both 2.4GHz and 5GHz, but it always seems to reject the connection when already having 8 connections.
The DHCP server is also not the problem, since the devices that won't properly connect are never even displayed in the LuCI interface.
Has anyone else had issues with this in the past, or is this a limit set by the Raspberry Pi developers?

It's a limit set by your hardware, namely its Broadcom fullmac wireless chipset (each connected client needs accounting, on-chip RAM in the wireless chipset, which only has enough to cover 8 clients). The RPi is not apt as wireless AP - and generations older than the RPi4 aren't good as wired router either.

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Would it be a better idea to use an external USB wifi adapter or a Pi 4 instead? I want to continue to use Raspberry Pis due to their small form factor.

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It would be a good idea to offload the wireless to a dedicated concurrent dual-band) AP (which might completely replace the RPi, if a RPi3 already suffices), which will be faster, longer range and not as limited. USB chipsets tend to suffer similar limits (4-8) as the sdio connected RPi wireless.

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