In OTL many attempts have been made over the decades trying to link a range of possible backers of Lee Harvey Oswald in his assassination of Kennedy, without proving more information than that certain groups had motives for opposing JFK and, potentially, acting outside the normal rules of engagement.
The following are some of the alternative timelines that can be developed: (JFK - John F Kennedy; LHO - Lee Harvey Oswald.)
Based on "named involvements"
1) The Cubans did it. On this being discovered the US takes pre-emptive action against the Cuban leadership for this act of war.
2) The Vietnamese did it. Outcome as 1) above
3) The Soviet leadership were involved. Discovery of this leads to war/a tactical strike on the Kremlin/other action. The People's Republic of China denounces the blatant provocation and there is a reaction from all other states and many international organisations. Disposing of leaders within the Soviet zone of influence, putting spies within the offices of senior administrative figures (Anthony Blunt, Willy Brandt) and similar is one thing - eliminating the head of state of the other superpower is an act of war.
4) The Mafia/other criminal groups did it. Discovery leads to a crackdown, and major action against anyone with any links to the organization that makes McCarthyism look like a tea party.
More general involvement
1) More generally "any group of persons being backers of LHO and so discovered." Immediate action, possibly disproportionate, taken against those involved.
2) (Combining with "alien involvement on Earth") JFK's statement about putting a man on the Moon is picked up by the aliens who have established a base there, and they decide to take action. The 'man on the grassy knoll' is actually teleported away.
3) A similar scenario to 2) involving time travellers - changing to their alt-history scenario for whatever reasons.
4) "The backers" of LHO decide to plant incriminating evidence that links him to "other groups"/gives him an overt motive (that lets them off the hook).
5) Persons wishing to manipulate the US political system to their advantage, consider JFK's private life, and decide that the best option is to exert pressure in an election year and beyond: the puppet on a string scenario.
Variants involving LHO
1) LHO leaves behind writings on 'Why I did it.' (This may well lead to a different set of theories.)
2) LHO is discovered setting the whole thing up before he can actually do anything.
3) LHO survives to go to trial/escapes to another country/goes underground.
4) LHO is shot by Jack Ruby (and possibly survives) - who gives a different set of reasons to that in OTL.
1) Another combination of injured and killed (JFK, Jackie Kennedy, John Connolly, the driver - which possibly leads to the car going out of control - etc).
- If Jackie Kennedy is killed, the equivalent of OTL 'Lady Diana cult' emerges.
- Several participants in the motorcade are killed. This leads to a general fear of a possible coup/attempt to destabilise the government (even though LHO has no such intention) and the police, the CIA and the FBI are innundated with information about "suspicious behaviour" and "information" on vast "conspiracies" etc. (The responses of J Edgar Hoover and Douglas MacArthur to the situation would have to be considered in this timeline)
2) LHO misses JFK, who eventually has an uphill struggle for re-election.
3) JFK is sufficiently injured to lead to a constitutional discussion on what to do with a President who is incapable in the long term of carrying out the duties of office.