diff --git a/CHANGES.markdown b/CHANGES.markdown
index ae69494..0f399e6 100644
--- a/CHANGES.markdown
+++ b/CHANGES.markdown
@@ -1,3 +1,7 @@
+## Changes in next [????.??.??]
+ - Backport new instances from GHC 9.10/`base-4.20`:
+   * `Fractional`, `RealFrac`, `Floating`, and `RealFloat` instances for `Compose`
+
 ## Changes in 0.9.1 [2023.10.11]
  - Backport new instances from GHC 9.8/`base-4.19`:
    * `Eq` and `Ord` instances for `SChar`, `SNat`, and `SSymbol`
diff --git a/README.markdown b/README.markdown
index a7ed79a..82621b0 100644
--- a/README.markdown
+++ b/README.markdown
@@ -60,7 +60,7 @@ To use `base-orphans`, simply `import Data.Orphans ()`.
  * `Eq` and `Ord` instances for `SChar`, `SNat`, and `SSymbol`
  * `Eq1`, `Read1`, and `Show1` instances for `Complex`
  * `Eq1`, `Ord1`, `Read1`, and `Show1` instances for `NonEmpty`
- * `Enum`, `Bounded`, `Num`, `Real`, and `Integral` instances for `Compose`
+ * `Enum`, `Bounded`, `Num`, `Real`, `Integral`, `Fractional`, `RealFrac`, `Floating`, and `RealFloat` instances for `Compose`
  * `Foldable` instance for `Either`, `(,)` and `Const`
  * `Foldable` and `Traversable` instances for `Alt` from `Data.Monoid`
  * `Functor`, `Applicative`, and `Monad` instances for
@@ -106,6 +106,7 @@ To use `base-orphans`, simply `import Data.Orphans ()`.
 
 ## Supported versions of GHC/`base`
 
+ * `ghc-9.10.*` / `base-4.20.*`
  * `ghc-9.8.*`  / `base-4.19.*`
  * `ghc-9.6.*`  / `base-4.18.*`
  * `ghc-9.4.*`  / `base-4.17.*`
diff --git a/src/Data/Orphans.hs b/src/Data/Orphans.hs
index eee3349..94b7b7c 100644
--- a/src/Data/Orphans.hs
+++ b/src/Data/Orphans.hs
@@ -94,7 +94,7 @@ import           GHC.ConsoleHandler as Console
 # endif
 #endif
 
-#if !(MIN_VERSION_base(4,19,0))
+#if !(MIN_VERSION_base(4,20,0))
 import           Data.Orphans.Prelude
 #endif
 
@@ -2050,6 +2050,25 @@ instance Ord (SSymbol s) where
 # endif
 #endif
 
+#if !(MIN_VERSION_base(4,20,0))
+# if MIN_VERSION_base(4,9,0)
+deriving instance Fractional (f (g a)) => Fractional (Compose f g a)
+deriving instance Floating (f (g a)) => Floating (Compose f g a)
+
+-- RealFrac and RealFloat both have Ord as a superclass. For the reasons stated
+-- above (near the Real/Integral instances for Compose), these
+-- RealFrace/RealFloat instances are slightly more complicated for older
+-- versions of base.
+#  if MIN_VERSION_base(4,18,0)
+deriving instance RealFrac (f (g a)) => RealFrac (Compose f g a)
+deriving instance RealFloat (f (g a)) => RealFloat (Compose f g a)
+#  else
+deriving instance (RealFrac (f (g a)), Ord1 f, Ord1 g, Ord a) => RealFrac (Compose f g a)
+deriving instance (RealFloat (f (g a)), Ord1 f, Ord1 g, Ord a) => RealFloat (Compose f g a)
+#  endif
+# endif
+#endif
+
 #if __GLASGOW_HASKELL__ < 710
 deriving instance Typeable  All
 deriving instance Typeable  AnnotationWrapper
diff --git a/src/Data/Orphans/Prelude.hs b/src/Data/Orphans/Prelude.hs
index 13e011a..571d543 100644
--- a/src/Data/Orphans/Prelude.hs
+++ b/src/Data/Orphans/Prelude.hs
@@ -21,7 +21,7 @@ This makes it much easier to be -Wall-compliant.
 Note that this module does not export any modules that could introduce name clashes.
 -}
 module Data.Orphans.Prelude
-#if MIN_VERSION_base(4,19,0)
+#if MIN_VERSION_base(4,20,0)
     () where
 #else
     ( module OrphansPrelude