There are some scenarios where it is necessary to us the full JTAG interface instead of the SWD interface to connect the DAP to the DUT, for example a JTAG daisy chain, a Cortex-A target like the Raspberry Pi, or when the older ARM7/ARM9/ARM11 chips gets involved. Is it possible to implement full JTAG on top of the current hardware and software?

JTAG uses a few existing SWD pins along with a few more:

• JTMS / SWDIO (Existing pin, bidirectional in SWD, output in JTAG, with pull up)
• JTCK / SWCLK (Existing pin, output with pull down)
• JTDI (new pin, output with pull up)
• JTDO / SWO (Existing pin, input with pull up)
• nJTRST (new pin, output with pull up)
• RTCK (new pin, input with pull down)

The RTCK pin worths some special mentioning: it is used on ARM7/ARM9/ARM11/Cortex-A chips to implement adaptive JTAG clocking. However this feature is entirely optional. You can just pull this pin down with a resistor and ignore it otherwise, if you have no plan on implementing JTAG adaptive clocking. There do exist some chips (like NXP LPC2103) that uses the pull down on RTCK to detect the presence of a debugger though.

https://github.com/devanlai/dap42 supports STM32F103 but no hardware design or just a mere pinout is available.