Interesting question, and indeed many attempts to do just this seem to indicate the answer 'no', a case in point being Tim Burton's abomination that is Planet Of The Apes. Should have left well alone.
However, sometimes things work out pretty well, and The Time Machine is a good example of this. It's directed by Simon Wells, the great-great grandson of H G Wells, who of course wrote the book on which the 1960 original is so faithfully based. This version takes a different slant, and as a result stands well on it's own. I thought it answered a few points well that were glossed over a little by Rod Taylor and Yvette Mimieux all those years before.
What about the story? Simple and believable. Hardtegen builds his time machine to go back and prevent his fiancee from being murdered on the night of their betrothal. But he can't stop it, because of the Cause and Effect paradox. So rather, he goes forwards in time to find answers as to why, and an accident in 2037 leaves him unconscious and hurtling forwards 800,000 years. There he finds two races, the peaceful, friendly Eloi, and the violent cave-dwelling Morlocks, for whom the Eloi exist only for sport and food. When Mara is taken on a hunting raid, Hardtegen does what the Eloi won't, and goes off to her rescue...........
American director who has directed four Steven Spielberg-produced animated features, including An American Tail: Fievel Goes West and The Prince of Egypt. Made his live-action debut with The Time Machine, a big budget adaptation of his great-grandfather H.G. Wells' novel. His expensive animation Mars Needs Moms was a notable financial disaster.