The Mr. Snuggles and the Dual Jason Theorem

For anyone that's seen Friday the 13th Parts V and VII (as well as the other 1-8) as well as for those unfortunate people who haven't, I would like to propose 2 theories.

1) The Mr. Snuggles Theorem. Through almost all of the Friday the 13th movies (and I'm referring to the classic 1-8, not this new rubbish), the film makers make it a point of showing a cat, which is in some way integral to the plot of the film. Why? What does this mean? The answer is simple. The answer comes from the fact that whoever finds the cat inevitably gets killed by Jason, and they are killed by Jason only when they experience a run in with the cat; therefore we can conclude that, as none of the victims or characters are known to have cats, the cat must belong to Jason. Due to the fact that Jason drowns as a boy, we can also determine that he, with his child-like mind, would give the cat a "warm and cheery" name, such as Mr. Snuggles.

2) The Dual Jason Theorem. Friday the 13th, Part V. According to the plot, we are supposed to believe that (SPOILER ALERT!!!!) the murders were committed by Roy, the paramedic whose son was killed at the Pinehurst facility, in order to avenge his son's killing. That is reasonable and more than explains the killing of the residents and staff of Pinehurst; however, it cannot explain the killings of Billy, Lana (who, funny/oddly enough, sees the cat), Vinnie, Pete, the drifter, Ethel, and Junior. None of them were directly involved with Pinehurst, and many if not all of them were unknowns for Roy. In fact, Vinnie and Pete only broke down near Pinehurst, and, as for Ethel and Junior, they were arguably more for the closing of Pinehurst than anyone. That being said, we can conclusively see that there were no viable reasons for killing them. If Roy did it, then there is entirely no motive for it. On the other hand, what if Roy didn't do it? What if Roy was (obliviously to him) acting in unison with the real Jason? Consider this: Roy had no known knowledge of the aforementioned people or their relations with Pinehurst and therefore no motive to kill them. Jason Voorhees himself is a recurring killer (in the same area), that kills in an indiscriminate fashion (as these murders were), and, on many occasions, kills people after their contact with his cat (as Lana had). These facts point to the only plausible solution, there are two Jasons, unknowingly acting at the same time.