Thanks, everyone, for your suggestions.

I solved it on my own. I just treated the input PDF file before signing.

The 100% working for me. Now the signature is showing on multiple pages horizontally.

If anyone is also facing the same issue, take the reference from the code.

        string src = @"C:\Test\inputFile.pdf";
        string dest = @"C:\Test\OutFile.pdf";

        var reader = new PdfReader(src);
        using (var fs = new FileStream(dest, FileMode.Create, FileAccess.Write))
        {
            // Create a new document. We'll set page size for each page individually.
            var doc = new Document();
            PdfWriter writer = PdfWriter.GetInstance(doc, fs);
            doc.Open();

            for (int i = 1, loopTo = reader.NumberOfPages; i <= loopTo; i++)
            {
                // Get page size with rotation applied (so width/height match visual)
                iTextSharp.text.Rectangle pageRect = reader.GetPageSizeWithRotation(i);
                // Use that as the new page size so orientation is preserved
                doc.SetPageSize(new iTextSharp.text.Rectangle(pageRect.Width, pageRect.Height));
                doc.NewPage();

                // Import the page from the source
                PdfImportedPage imported = writer.GetImportedPage(reader, i);
                PdfContentByte cb = writer.DirectContent;

                // Get original rotation (0, 90, 180, 270)
                int rot = reader.GetPageRotation(i) % 360;

                // Add the imported page with a transform that cancels the rotation
                switch (rot)
                {
                    case 90:
                        {
                            // rotate -90 (or counter-rotate) so content appears same but writer page has no /Rotate
                            cb.AddTemplate(imported, 0, -1, 1, 0, 0, pageRect.Height);
                            break;
                        }
                    case 180:
                        {
                            cb.AddTemplate(imported, -1, 0, 0, -1, pageRect.Width, pageRect.Height);
                            break;
                        }
                    case 270:
                        {
                            cb.AddTemplate(imported, 0, 1, -1, 0, pageRect.Width, 0);
                            break;
                        }

                    default:
                        {
                            // no rotation, normal placement
                            cb.AddTemplate(imported, 1, 0, 0, 1, 0, 0);
                            break;
                        }
                }
            }

            doc.Close();
            writer.Close();
        }
        reader.Close();