There are a lot of Black / White wires in that connector that are joined together. The Bk/white wires typically provide power for various components. I haven't studied it closely, but I would imagine that one of the thicker gauge wires is the one that provides the power. The others redistribute it.
The melting body suggests too much heat being generated by one of the terminals - ie too much current passing through it. This may be due to corrosion / higher resistance, but it is also possible that a previous owner has tapped into power from one or more of bk/wh leads, not considering the total current that has to pass through just one of those terminals.
Bottom line - check what extras have been fitted, and where they are getting their power from.
NB this may also apply to a similar connector that connects the earth wires together.
The power for this connector seems to come from the 20A fuse labelled FI-Ignition Coils-Fuel Pump, and is turned on by the bank angle sensor relay. The same power source feeds a lot of relays and sensors and other devices such as the PAIR solenoid. I doubt that there is much spare capacity on the wiring, fuse or the terminals in that connector.