Have a button in adobe [Acrobat] that adds a row of columns, then adds another row below it.

Certainly, to achieve the desired functionality of adding a new row of text fields each time the button is clicked, you can modify your code as follows:

var myRows = new Array();
var rowCounter = 1;

function addRow() {
    myRows[rowCounter - 1] = "Row" + rowCounter + ".Column1";
    myRows[rowCounter] = "Row" + rowCounter + ".Column2";
    myRows[rowCounter + 1] = "Row" + rowCounter + ".Column3";
    myRows[rowCounter + 2] = "Row" + rowCounter + ".Column4";

    var coordinates = [10, 136 + (rowCounter * 24)]; // Adjust the vertical position for each new row
    var w = 144;
    var h = 18;
    var wGap = 6;
    var afields = [coordinates[0], coordinates[1], coordinates[0] + w, coordinates[1] - h];

    for (var i = 0; i < myRows.length; i++) {
        this.addField(myRows[i], "text", 0, afields);
        afields[0] += (w + wGap);
        afields[2] += (w + wGap);
    }

    rowCounter += 1;
}

// Call this function when the button is clicked
addRow();

Yes, you can do this by restructuring the code to make the field names and the positioning programmable. 

For example, the loop needs to be setup to count rows and columns, then the field names will be built dynamically based on the row/column. Same for the field rectangle.

This code is untested. I just wrote it as an example of how it can be done. You'll need to do debug.

var nXStart = 10, nYStart = 136;
var nFldWidth = 144;
var nFldHeight = 18;
var nHorzGap = 6;
var nVertGap = 6;
var xPos, nYPos,rctFld ;
var nMaxRows = 4;
for(var nRow=1;nRow<=nMaxRows;nRow++)
{
     xPos=nXStart;
     for (var nCol=1; nCol<=4; nCol++)
     {
          rctFld = [x,y,x+nFldWidth, y-nFldHeight];
          var f = this.addField("Row" + nRow + ".Col" + nCol, "text", 0, rctFld );
          xPos += nHorzGap + nFldWidth;
     }
     yPos -= nVertGap + nFldHeight;
}

Hi @Coleman_1211 

Since your question is about Adobe Acrobat, I have moved this from the "Using the Community" forum where you posted.

~ Jane