In this special case where AnotherTable1 is joined in both when parts with the same condition you only need three left joins:
SELECT table1.a,
table2.b,
CASE
WHEN table1.XY = 1 THEN
?.something -- from whereever it's coming
WHEN table1.XY = 2 THEN
?.something -- from whereever it's coming
END AS [problem]
FROM MyTable1 table1
INNER JOIN MyTable2 table2
ON table1.a = table2.b
LEFT JOIN AnotherTable1 at1
ON at1.abc = table2.abc
LEFT JOIN AnotherTable2 at2
ON at1.x = at2.y
LEFT JOIN AnotherTable3 at3
ON at1.x = at3.y
In more general case you would have this option
FROM MyTable1 table1
INNER JOIN MyTable2 table2
ON table1.a = table2.b
LEFT JOIN
(select *
from AnotherTable1 at1
INNER JOIN
AnotherTable2 at2
ON at1.x = at2.y
) at1
ON at1.abc = table2.abc
...