public bool Intersection {get; set;}

layerList = MapView.Active.Map.GetLayersAsFlattenedList().OfType<FeatureLayer>();

// configure by layer
foreach (var layer in layerList)
{
  // find the state of the snapModes for the layer
  var lsm = ArcGIS.Desktop.Mapping.Snapping.GetLayerSnapModes(layer);
  bool vertexOn = lsm.Vertex;
  // or use 
  vertexOn = lsm.GetSnapMode(SnapMode.Vertex);

  bool edgeOn = lsm.Edge;
  // or use 
  edgeOn = lsm.GetSnapMode(SnapMode.Edge);

  bool endOn = lsm.End;
  // or use 
  endOn = lsm.GetSnapMode(SnapMode.End);

  // update a few snapModes 
  //   turn Vertex off
  lsm.SetSnapMode(SnapMode.Vertex, false);
  // intersections on
  lsm.SetSnapMode(SnapMode.Intersection, true);

  // and set back to the layer
  ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(layer, lsm);


  // assign a single snap mode at once
  ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(layer, SnapMode.Vertex, false);


  // turn ALL snapModes on
  ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(layer, true);
  // turn ALL snapModes off
  ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(layer, false);
}


// configure for a set of layers

// set Vertex, edge, end on for a set of layers, other snapModes false
var vee = new LayerSnapModes(false);
vee.Vertex = true;
vee.Edge = true;
vee.End = true;
ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(layerList, vee);


// ensure intersection is on for a set of layers without changing any other snapModes

// get the layer snapModes for the set of layers
var dictLSM = ArcGIS.Desktop.Mapping.Snapping.GetLayerSnapModes(layerList);
foreach (var layer in dictLSM.Keys)
{
  var lsm = dictLSM[layer];
  lsm.Intersection = true;
}
ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(dictLSM);


// set all snapModes off for a list of layers
ArcGIS.Desktop.Mapping.Snapping.SetLayerSnapModes(layerList, false);