Which does complicate the reviewing process since this is, like The Lord of the Rings, one book sliced into three volumes.
Anyway, it opens in the modern day -- at one point Miranda has clearly seen Who Framed Roger Rabbit -- with her receiving a message from her father to warn her brothers and sister, who were all born after the events in The Tempest. (Which William Shakespeare fictionalized. She didn't, for instance, marry Ferdinard.)
This is complicated. Since Prospero retired, she has been running Prospero, Inc., which persuades salamanders, djinni, etc. to refrain from causing natural disasters by paying them with phoenix ash and other treasures. Her siblings have all left the workings of the company -- especially since one of them died -- and she's not on good terms with them either. (Note, you may find Miranda to be somewhat cold in the opening. This will prove to be of great significance.)
Prospero, Inc.'s detective, Mab (an air spirit like Ariel, incarnated in a human body) recommends against the search. When she insists, and they talk of the siblings' natures so he can, they are attacked by the Three Shadowed Ones that Prospero mentioned in his note. Mab agrees that searching should be done.
Whereupon they set out in search into a world which includes Greek mythology; The Tempest as somewhat accurate; the Fair Folk with an origin taken from folklore, being not quite all the way fallen angels; Miranda's Lady, to whom she was dedicated as a child; her sister's island, where she changes old lover and others to beasts; a maenad and a harpy doing the cooking; a cat's explanation of the Eleusanian mysteries as trying to learn the secret of cats; Father Christmas, and the Scrying Pool of Naughty and Nice; an order founded by Solomon; her insane brother Mephisto, who is sometimes great fun, and sometimes -- well, his mansion is littered with Post-It notes reminded him of all sorts of things; the use of family magical staffs against them, which does not always work out so well; a winged lion; something that is not quite a cat but nevertheless gives the impression of one; her brother Theo's determination to age to death to avoid magic; and an old flame who turns out not to be what he seemed -- more than once.
In fact, discoveries in this story usually turn out to be discovering something that will itself be overturned when you make more discoveries. Sometimes back to the original, sometimes boldly onward to still new stuff -- they were still making major discoveries almost up to the end of Prospero In Hell. And the break there will not continue, since the blurb for the third promises that Miranda will learn the truth about many things. It's a fascinatingly complex structure of discoveries.