Execute Copy Parallel on a selected line feature with the set offset value while in the editing session in ArcMap. Will create multiple features using the interval values set.

CopyParallelsExecuteClass.cs

using System;
using System.Collections.Generic;
using System.Text;
using System.IO;
using ESRI.ArcGIS.esriSystem;
using ESRI.ArcGIS.Framework;
using ESRI.ArcGIS.Editor;
using ESRI.ArcGIS.Geodatabase;
using ESRI.ArcGIS.Geometry;

namespace CopyParallels
{
    public class CopyParallelsExecuteClass : ESRI.ArcGIS.Desktop.AddIns.Button
    {
        public CopyParallelsExecuteClass()
        {
        }

        private void DoCopyParallel(IFeatureClass fc, IFeature f, int startValue, int endValue, int stepValue, int side)
        {
            for (int offsetValue = startValue; offsetValue <= endValue; offsetValue = offsetValue + stepValue)
            {
                //Interface to do a "copy parallel"
                IConstructCurve3 construct = new PolylineClass();

                //How to construct
                object offset = esriConstructOffsetEnum.esriConstructOffsetMitered;

                IPolyline source = f.Shape as IPolyline;

                //Side determines left/right with -1/+1
                construct.ConstructOffset(source, offsetValue * side, ref offset);

                //Storing output shape
                IFeature newFeature = fc.CreateFeature();
                newFeature.Shape = (IGeometry)construct;
                newFeature.Store();
            }

            return;
        }

        protected override void OnClick()
        {
            //Read and parse user values
            string V = IntervalsSetterComboBox.comboValue;
            string[] Arr = V.Split(',');
            int startValue = Convert.ToInt16(Arr[0]);
            int endValue = Convert.ToInt16(Arr[1]);
            int stepValue = Convert.ToInt16(Arr[2]);
                        
            //Get the editor
            UID uid = new UIDClass();
            uid.Value = "esriEditor.Editor";

            IEditor editor;
            editor = (IEditor)ArcMap.Application.FindExtensionByCLSID(uid);

            //Get selected feature
            IEnumFeature enumfeature = editor.EditSelection;
            IFeature f = enumfeature.Next();

            //For adding a new feature
            IFeatureClass fc = f.Class as IFeatureClass;

            //Start an editing operation for undo/redo
            editor.StartOperation();

            DoCopyParallel(fc, f, startValue, endValue, stepValue, 1);
            DoCopyParallel(fc, f, startValue, endValue, stepValue, -1);
            
            editor.StopOperation("Copy Parallel");

            //Refresh map
            ArcMap.Document.ActiveView.Refresh();

        }
        protected override void OnUpdate()
        {
            Enabled = ArcMap.Application != null;
        }
    }

}

IntervalsSetterComboBox.cs

using System;
using System.Collections.Generic;
using System.Text;
using System.IO;

namespace CopyParallels
{
    public class IntervalsSetterComboBox : ESRI.ArcGIS.Desktop.AddIns.ComboBox
    {
        public static string comboValue;  

        public IntervalsSetterComboBox()
        {
        }

        protected override void OnUpdate()
        {
            Enabled = ArcMap.Application != null;
            
            comboValue = Value;
        }
    }

}