Gakken's "The IJA aircraft" says that Ki-99 was the IJA and the IJN's joint program ordered to Mitsubishi in 5/7/1943 by document name 航密第8476号(Secret or pressurized cabin aircraft development order No.8476?).
Perhaps 航 means 航空機(The aircraft) and 密 means 秘密(secret) or 気密(pressurized cabin).
Ki-99 was a single seat single engine short range fighter with Ha-211 engine(Mitsubishi Ha-43(MK9) engine), two 30mm cannon and two 20mm cannon.
This project was cancelled in May 1944 due to slow development speed.
Mitsubishi Ha-43 engine.
http://www.secretprojects.co.uk/forum/index.php?topic=21030.0
Basically MK9 engine was a high altitude engine.
MK9A : With turbocharger, intercooler and forced cooling fan ; Ki-83, A7M3-J, Manshu Ki-98, Manshu Ki-65?, Mitsubishi Ki-99?
(MK9A without turbocharger, intercooler and forced cooling fan type ; A7M2 Reppu)
MK9B : With Valkan coupling drive first stage supercharger and mechanical drive Second stage supercharger ; Kawanishi J3K1, A7M2-J, Kawanishi N1K5-J?
MK9C : With single stage three speed mechanical super charger ; A7M3
MK9D : Pusher type MK9B ; J7W Shinden
I imagine that there were some relation between Ki-99 and Reppu(also once called Reppu -kai) A7M2-J with MK9B engine, Reppu-kai A7M3-J with MK9A engine,Reppu A7M3(temporaly name three speed Reppu) with MK9C engine and Manshu Ki-65.
I imagine that A7M2-J nose shape looks like Kawanishi N1K5-J.
http://www.secretprojects.co.uk/forum/index.php?action=dlattach;topic=4802.0;attach=564797;image
Fate of Ki-99 looks like fate of J6K. ;D