The following example is from the Longman Dictionary of Common Errors. It marks the first as wrong and the latter two as correct.
✗ They had already ten children and didn't want any more.
✔ They already had ten children and didn't want any more.
✔ They had ten children already and didn't want any more.
Does this classification correspond with your experience? To my ears, "had already ten" sounds fine.
edit: My native language is German, where "Sie hatten bereits zehn Kinder" is the default sentence structure.