From section 27.2(*) of the Atmega328xx data sheet (emphasis mine):

In ATmega88A/88PA/168A/168PA/328/328P the Boot Loader Support provides a real Read-While-Write Self- Programming mechanism for downloading and uploading program code by the MCU itself. This feature allows flexible application software updates controlled by the MCU using a Flash-resident Boot Loader program. The Boot Loader program can use any available data interface and associated protocol to read code and write (program) that code into the Flash memory, or read the code from the program memory. The program code within the Boot Loader section has the capability to write into the entire Flash, including the Boot Loader memory. The Boot Loader can thus even modify itself, and it can also erase itself from the code if the feature is not needed anymore. The size of the Boot Loader memory is configurable with fuses and the Boot Loader has two separate sets of Boot Lock bits which can be set independently. This gives the user a unique flexibility to select different levels of protection.

You may need to re-write the input section of the bootloader, but it sure sounds like Atmel intended it to be doable.

• My data-sheet is dated 2018; the relevant section, Section 27, is titled "Boot Loader Support – Read-While-Write Self-Programming", in case a later revision has different section numbers.

From section 27.2(*) of the Atmega328xx data sheet (emphasis mine):

In ATmega88A/88PA/168A/168PA/328/328P the Boot Loader Support provides a real Read-While-Write Self- Programming mechanism for downloading and uploading program code by the MCU itself. This feature allows flexible application software updates controlled by the MCU using a Flash-resident Boot Loader program. The Boot Loader program can use any available data interface and associated protocol to read code and write (program) that code into the Flash memory, or read the code from the program memory. The program code within the Boot Loader section has the capability to write into the entire Flash, including the Boot Loader memory. The Boot Loader can thus even modify itself, and it can also erase itself from the code if the feature is not needed anymore. The size of the Boot Loader memory is configurable with fuses and the Boot Loader has two separate sets of Boot Lock bits which can be set independently. This gives the user a unique flexibility to select different levels of protection.

You may need to re-write the input section of the bootloader, but it sure sounds like Atmel intended it to be doable.

[*] My data-sheet is dated 2018; the relevant section, Section 27, is titled "Boot Loader Support – Read-While-Write Self-Programming", in case a later revision has different section numbers.