As it turns out, of course, Regan and Goneril show their true colours fairly soon and refuse to take care of Lear and end up plotting against each other for sole control of the kingdom.
In Shakespeare's version of events a third character, Edward, the illegitimate son of the Earl of Gloucester, is the one who contrives to set the two daughters against each other by feigning love for both of them. In the version of events as narrated by Pocket, Fool (or Court Jester as we'd call him) to the court of King Lear, he's the puppet master behind the scenes doing his best to manipulate events.
Unfortunately too many of his puppets have minds of their own and his plans quickly go awry. Initially he had hoped to ensure that Cordelia, his favourite among the three sisters, would remain at home in England and not be married off to a foreign prince, and when that fails he's left scrambling to find ways to make things right.
While Moore adheres pretty much to the storyline of Lear as Shakespeare wrote it, it doesn't stop him from adding in a few extras from other plays as well. There's a vengeful ghost, shades of Hamlet (because there's always a "bloody ghost"), as well as a couple of guest appearances from the three witches of Macbeth, Parsley, Sage, and Rosemary, ("What no Thyme" said Kent. "We've the got the time if you've got the inclination") to help propel the plot along.
Of course the major difference between the original and Moore's version is the tone; instead of Lear the tragic hero undone by his flaw of vanity as the main theme we are treated to a ribald adventure along the lines of The Decameron.
In most instances, when a modern writer attempts to satirize Shakespeare they fall flat, because no matter what they do their efforts pale in comparison to the original. What separates Moore's effort from any of the others that I've read is the fact he is able to reproduce the tone and spirit of the original in his use of language. Even though he is writing in mainly modern vernacular when his characters resort to bawdy language he draws upon the vast and colourful vocabulary of Elizabethan England giving them a verisimilitude lacking in most modern attempts at creating characters from this time period.