Copy Only Columns That Have Certain Values?

I have a worksheet with values that change weekly (sample, attached). The number of rows and columns may change as well. However, columns A, B, and C will always have date, name and location data and therefore must be preserved. Aside from the headers, the values in the columns from D onward will include only the numbers 0, 1, 2, or 3.

I need to copy the columns to Sheet2 and then delete all of the columns from D onward that do not have a 2 or a 3 in them. In other words, I need to always keep columns A, B, and C, and also keep any column (and all of its data) if a 2 and/or 3 shows up anywhere in the column.

I imagine there is even a quicker way to cherry pick the first three columns, as well as any other columns that have a 2 or 3 in them, and then paste them to the second worksheet. However, either approach will meet the need well enough.