where to start............as far as why michael needed "more cleansing" if you remember in the beginning when Abbandando is talking to the press about the award that michael has just received the press continues to bring up michael's past. right there it shows us that even after such a high honor is given to michael, it stil isnt good enough to clear his name.
ABBANDANDO
The order of Saint Sebastian is one of the highest honors the Catholic Church can bestow upon a layman. The award was first granted by Pope Gregory…

REPORTER
What about Mr. Corleone’s connections with Las Vegas gambling?

ABBANDANDO
Presskits have pictures of…

REPORTER
what about his involvements with the underworld?

ABBANDANDO
Hey, cut the crap, huh? The Pope -- the Holy Father himself -- has this very day blessed Michael Corleone; and you think you know better than the Pope?
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immobliare is explained when michael is talking to the archbishop.
"Largest landlord on earth, real estate all over the world worth six billion dollars." which the church owns 25% of

its a purely legitimate money maker. mike was looking for a better to make his family the most powerful, he wanted to take the family in the right direction. cleansing his family name through the relationship with the church and its relation to immobliare.

altobello was the peacemaker, i believe he was a negotiator for lucchessi and the muscle lucchessi needed to be powerful. first joey zasa was called upon from altobello to take care of michael for lucchessi as michael was starting to understand that this vatican bank was very corrupt. zasa was looked down upon by most don's as a low life so he knew that he would never get away with killing michael and being respected for it, so he orders the massacre that get's rid of all his enemies.
michael lives thru the blood bath.....he wants to write to zasa in hopes to keep zasa close to find out more about who is really against because he knows zasa is just muscle and would have nerve to pull off something like this without the backing
"our true enemy has not shown his face"
vincent lets his temper get the best of him and kills zasa, there goes michaels informant.......but then he remembers altobello had survived the massacre because he made a "deal" with zasa. so he must know something.......they both retire to sicily, michael has hopes of finding out more about whos against him and stopping him from rising up, and how involved altobello happens to be. altobello has hopes of bringing the bate, that survived the massacre, to luchessi out in sicily in hopes to better his postion
after the meeting with don tommasino mike finds out that altobello is just the peacemaker between this unknown enemy and the muscle. he also finds out that this unknown enemy that wants michael gone is lucchessi. luchessi controls the archbishop gilday, swiss banker, and altobello all in a plot to gain more money
mike asks vincent to betray him to find out how deep altobello is involved. after vincent is introduced to lucchessi through altobello, vincent finds out that altobello "banked" joey for lucchessi and calls vincent the "hero" that put joey to his grave.....IMO joey failed at his primary goal, which was to get rid of michael, so they understand he's useless now, vincent kills joey and now lucchessi is rid of this useless muscle.

altobello, now under the impression that vincent will work him and lucchessi, decides to take manners into his own hands making him the hero and not taking the chance of relying on another muscle to screw things up a again. he hires an assassin to do the job right, and understanding that mary takes control of immobliare if mike dies, he asks the assassin to "take of 2 stones" to rid the corleone family of any control
DON ALTOBELLO
"You are my ‘ace in the hole,’ as we say in America. I have a stone in my shoe. You can remove it."
MOSCA
"Only one stone?"

these are all theories, it just helps me understand the story more...........remember just opinions