LINQ to SQL: Multiple joins ON multiple Columns. Is this possible?

Joining on multiple columns in Linq to SQL is a little different.

var query =
    from t1 in myTABLE1List // List<TABLE_1>
    join t2 in myTABLE1List
      on new { t1.ColumnA, t1.ColumnB } equals new { t2.ColumnA, t2.ColumnB }
    ...

You have to take advantage of anonymous types and compose a type for the multiple columns you wish to compare against.

This seems confusing at first but once you get acquainted with the way the SQL is composed from the expressions it will make a lot more sense, under the covers this will generate the type of join you are looking for.

EDIT Adding example for second join based on comment.

var query =
    from t1 in myTABLE1List // List<TABLE_1>
    join t2 in myTABLE1List
      on new { A = t1.ColumnA, B = t1.ColumnB } equals new { A = t2.ColumnA, B = t2.ColumnB }
    join t3 in myTABLE1List
      on new { A = t2.ColumnA, B =  t2.ColumnB } equals new { A = t3.ColumnA, B = t3.ColumnB }
    ...

U can also use :

var query =
    from t1 in myTABLE1List 
    join t2 in myTABLE1List
      on new { ColA=t1.ColumnA, ColB=t1.ColumnB } equals new { ColA=t2.ColumnA, ColB=t2.ColumnB }
    join t3 in myTABLE1List
      on new {ColC=t2.ColumnA, ColD=t2.ColumnB } equals new { ColC=t3.ColumnA, ColD=t3.ColumnB }