Append data from four tables into one new table

It sounds like Power Query is trying to fold the queries back to the MySQL source, and MySQL cannot handle a UNION statement with more than 2 tables.

To fix this, break folding. To do this, go to each table you want to append and in the last step, wrap it with Table.Buffer(). 

So if the last step is something like:

Table.AddColumn(#"Changed Type", "Total", each [Cost] + [Tax])

Make it

Table.Buffer(Table.AddColumn(#"Changed Type", "Total", each [Cost] + [Tax]))

Then Power Query will do the combinations in the mashup engine vs asking the server to do it.