I enjoy Palladium games, especially the settings.   I have no issue with the D20 for combat and D100 for skills and I skip most of the fiddly rules in-between.   However, I have not enjoyed how Attacks Per Melee work.  

Here is what I have done.  

1) Your current "Attacks per Melee" becomes "Bonus Actions Per Combat" so if you have 5 Attacks, you now have 5 Bonus Actions.   Mooks only gain Bonus Actions based on advances given by their H2H combat so most mooks won't have Bonus Actions.  Boxing does not give you a Bonus action.

2) Everyone has one action per melee round.  If you want more actions, you spend a Bonus Action chip.

3) Normally, you can only spend one Bonus Action per melee.   However, if your H2H combat training has granted additional attacks, you can spend that many Bonus Actions per melee.  AKA, if your Martial Arts give you +1 Attack at 3rd level, then you could spend up to 2 Bonus Actions in a single melee (total 3 actions).

4) As always, Parry is a free action.   However, Roll with Punch/Impact takes an action.   You can choose to Roll instead of attempting to Parry as a free action.  I am toying with letting Simultaneous Attack be a free action as well, but an SA would be Wild Blow (aka, D20 w/o modifier)

5) Bonus Actions reset after each combat.

The end result is this.  Most 1st level PCs have 4 bonus actions and by 5th level, most have 6 bonus actions.  Enough to dodge when you feel you have the chance, but not so many that you will be tossing them willy-nilly.   It also creates a nice ebb and flow for when characters save their actions for later in the battle versus those who start off with a big bang.

I am toying with making Automatic Dodge into a once-per-melee round ability instead of having the Juicer get a free dodge roll against every blow.   It still keeps the ability very powerful because a combat that goes 4 rounds means you just got 4 free Bonus Actions that don't count toward your per-melee limit.

I am also toying with treating Bonus Action chips as Luck chips so players can spend them as a re-roll.   I do that with Action Points in 4e and its worked great.