An insert piece for a blood tubing set, comprising at least, respectively, - a first connection site for connecting a first tubing portion of the blood tubing set to the insert piece; - a second connection site for connecting a second tubing portion of the blood tubing set to the insert piece; - a third connection site for connecting a third tubing portion of the blood tubing set to the insert piece; - a first main line for conducting blood as a first liquid through the insert piece, wherein the first main line is in fluid communication with the first connection site and with the second connection site; - a second main line for conducting blood as the first liquid through the insert piece, wherein the second main line is in fluid communication with the first connection site and with the second connection site; - a connection portion which connects both main lines (107a, 107b) to each other or to the second connection site; - a secondary line for conducting a second liquid, preferably an infusion, into at least one of the first main line; the second main line; and the connection portion; wherein - the secondary line is in fluid communication with the third connection site; - the first connection site comprises a perfusable lumen having a first cross section area; - the second connection site comprises a perfusable lumen having a second cross section area; - the first main line and/or the second main line comprises a perfusable lumen having a third cross section area; and - the first main line and the second main line being arranged such that fluid is conducted through the insert piece either through the first main line or the second main line. - a first connection site for connecting a first tubing portion of the blood tubing set to the insert piece; - a second connection site for connecting a second tubing portion of the blood tubing set to the insert piece; - a third connection site for connecting a third tubing portion of the blood tubing set to the insert piece; - a first main line for conducting blood as a first liquid through the insert piece, wherein the first main line is in fluid communication with the first connection site and with the second connection site; - a second main line for conducting blood as the first liquid through the insert piece, wherein the second main line is in fluid communication with the first connection site and with the second connection site; - a connection portion which connects both main lines (107a, 107b) to each other or to the second connection site; - a secondary line for conducting a second liquid, preferably an infusion, into at least one of the first main line; the second main line; and the connection portion; wherein the first main line; the second main line; and the connection portion; wherein - the secondary line is in fluid communication with the third connection site; - the first connection site comprises a perfusable lumen having a first cross section area; - the second connection site comprises a perfusable lumen having a second cross section area; - the first main line and/or the second main line comprises a perfusable lumen having a third cross section area; and - the first main line and the second main line being arranged such that fluid is conducted through the insert piece either through the first main line or the second main line.