Yes it does.
It exists an open source Software for Minipro TL866 by David Griffith
You can get it on gitlab.
https://gitlab.com/DavidGriffith/minipro/This should be the latest aktive repository as far as i know.
There exist no Executable. Must compile it by yourself.
The Atmega32u is not in the device.h list so this Software don't yet support your Chip also.
I don't know other actual software projects than this one.
In this case you must use an other prgrammer for the ATMEGA32U2.
Mini Pro and the Plus Version can't yet do that. That's fact.
I am not familiar with the ATMEGA32U2
so i don't know an appropriate programmer you can use.
Some googeling gave me results for an ATmega32U2 USB Development Board for about 16 bucks.
Software to use is "FLIP".