diff --git a/src/pals/parameters/MagneticMultipoleParameters.py b/src/pals/parameters/MagneticMultipoleParameters.py
index a1b7dd0..7c4b176 100644
--- a/src/pals/parameters/MagneticMultipoleParameters.py
+++ b/src/pals/parameters/MagneticMultipoleParameters.py
@@ -1,62 +1,67 @@
 from pydantic import BaseModel, ConfigDict, model_validator
-from typing import Any, Dict
+from typing import Any
+
+# Valid parameter prefixes, their expected format and description
+_PARAMETER_PREFIXES = {
+    "tilt": ("tiltN", "Tilt"),
+    "Bn": ("BnN", "Normal component"),
+    "Bs": ("BsN", "Skew component"),
+    "Kn": ("KnN", "Normalized normal component"),
+    "Ks": ("KsN", "Normalized skew component"),
+}
+
+
+def _validate_order(
+    key_num: str, parameter_name: str, prefix: str, expected_format: str
+) -> None:
+    """Validate that the order number is a non-negative integer without leading zeros."""
+    error_msg = (
+        f"Invalid {parameter_name}: '{prefix}{key_num}'. "
+        f"Parameter must be of the form '{expected_format}', where 'N' is a non-negative integer without leading zeros."
+    )
+    if not key_num.isdigit() or (key_num.startswith("0") and key_num != "0"):
+        raise ValueError(error_msg)
 
 
 class MagneticMultipoleParameters(BaseModel):
-    """Magnetic multipole parameters"""
+    """Magnetic multipole parameters
 
-    # Allow arbitrary fields
-    model_config = ConfigDict(extra="allow")
+    Valid parameter formats:
+    - tiltN: Tilt of Nth order multipole
+    - BnN: Normal component of Nth order multipole
+    - BsN: Skew component of Nth order multipole
+    - KnN: Normalized normal component of Nth order multipole
+    - KsN: Normalized skew component of Nth order multipole
+    - *NL: Length-integrated versions of components (e.g., Bn3L, KsNL)
+
+    Where N is a positive integer without leading zeros (except "0" itself).
+    """
 
-    # Custom validation of magnetic multipole order
-    def _validate_order(key_num, msg):
-        if key_num.isdigit():
-            if key_num.startswith("0") and key_num != "0":
-                raise ValueError(msg)
-        else:
-            raise ValueError(msg)
+    model_config = ConfigDict(extra="allow")
 
-    # Custom validation to be applied before standard validation
     @model_validator(mode="before")
-    def validate(cls, values: Dict[str, Any]) -> Dict[str, Any]:
-        # loop over all attributes
+    @classmethod
+    def validate(cls, values: dict[str, Any]) -> dict[str, Any]:
+        """Validate all parameter names match the expected multipole format."""
         for key in values:
-            # validate tilt parameters 'tiltN'
-            if key.startswith("tilt"):
-                key_num = key[4:]
-                msg = " ".join(
-                    [
-                        f"Invalid tilt parameter: '{key}'.",
-                        "Tilt parameter must be of the form 'tiltN', where 'N' is an integer.",
-                    ]
-                )
-                cls._validate_order(key_num, msg)
-            # validate normal component parameters 'BnN'
-            elif key.startswith("Bn"):
-                key_num = key[2:]
-                msg = " ".join(
-                    [
-                        f"Invalid normal component parameter: '{key}'.",
-                        "Normal component parameter must be of the form 'BnN', where 'N' is an integer.",
-                    ]
-                )
-                cls._validate_order(key_num, msg)
-            # validate skew component parameters 'BsN'
-            elif key.startswith("Bs"):
-                key_num = key[2:]
-                msg = " ".join(
-                    [
-                        f"Invalid skew component parameter: '{key}'.",
-                        "Skew component parameter must be of the form 'BsN', where 'N' is an integer.",
-                    ]
-                )
-                cls._validate_order(key_num, msg)
+            # Check if key ends with 'L' for length-integrated values
+            is_length_integrated = key.endswith("L")
+            base_key = key[:-1] if is_length_integrated else key
+
+            # No length-integrated values allowed for tilt parameter
+            if is_length_integrated and base_key.startswith("tilt"):
+                raise ValueError(f"Invalid magnetic multipole parameter: '{key}'. ")
+
+            # Find matching prefix
+            for prefix, (expected_format, description) in _PARAMETER_PREFIXES.items():
+                if base_key.startswith(prefix):
+                    key_num = base_key[len(prefix) :]
+                    _validate_order(key_num, description, prefix, expected_format)
+                    break
             else:
-                msg = " ".join(
-                    [
-                        f"Invalid magnetic multipole parameter: '{key}'.",
-                        "Magnetic multipole parameters must be of the form 'tiltN', 'BnN', or 'BsN', where 'N' is an integer.",
-                    ]
+                raise ValueError(
+                    f"Invalid magnetic multipole parameter: '{key}'. "
+                    f"Parameters must be of the form 'tiltN', 'BnN', 'BsN', 'KnN', or 'KsN' "
+                    f"(with optional 'L' suffix for length-integrated), where 'N' is a non-negative integer."
                 )
-                raise ValueError(msg)
         return values
diff --git a/tests/test_parameters.py b/tests/test_parameters.py
index 21eb8f9..ba904e9 100644
--- a/tests/test_parameters.py
+++ b/tests/test_parameters.py
@@ -43,10 +43,19 @@ def test_ParameterClasses():
     # assert emp.En1 == 1.0
 
     # Test MagneticMultipoleParameters
-    mmp = MagneticMultipoleParameters(Bn1=1.0, Bs1=0.5)
+    mmp = MagneticMultipoleParameters(tilt1=1.2, Bn1=1.0, Bs1=0.5)
+    assert mmp.tilt1 == 1.2
     assert mmp.Bn1 == 1.0
     assert mmp.Bs1 == 0.5
 
+    mmp2 = MagneticMultipoleParameters(Kn0=1.0, Ks1=0.5)
+    assert mmp2.Kn0 == 1.0
+    assert mmp2.Ks1 == 0.5
+
+    mmp3 = MagneticMultipoleParameters(Bn1L=1.0, Bs1L=0.5)
+    assert mmp3.Bn1L == 1.0
+    assert mmp3.Bs1L == 0.5
+
     #  catch typos
     with pytest.raises(ValidationError):
         _ = MagneticMultipoleParameters(Bm1=1.0, Bs1=0.5)
@@ -54,6 +63,10 @@ def test_ParameterClasses():
         _ = MagneticMultipoleParameters(Bn1=1.0, Bv1=0.5)
     with pytest.raises(ValidationError):
         _ = MagneticMultipoleParameters(Bn01=1.0, Bs01=0.5)
+    with pytest.raises(ValidationError):
+        _ = MagneticMultipoleParameters(Bn1v=1.0, Bs1l=0.5)
+    with pytest.raises(ValidationError):
+        _ = MagneticMultipoleParameters(tilt1L=1.2)
 
     # Test SolenoidParameters
     sol = SolenoidParameters(Ksol=0.1, Bsol=0.2)