You can send your data like the "POST" request through the "HEADERS".
Something like this:
$.ajax({
url: "htttp://api.com/entity/list($body)",
type: "GET",
headers: ['id1':1, 'id2':2, 'id3':3],
data: "",
contentType: "text/plain",
dataType: "json",
success: onSuccess,
error: onError
});