Meta analysis has shown that multi-lumen CVC has more infections than single lumen. (Article Rates of infection for single-lumen versus multilumen centra...
) But studies comparing double and triple lumen are less.
You can also go through: https://infekt.ch/content/uploads/2013/11/Templeton_2008_Multiumen.pdf
Each time you access the CVC you risk introducing infection. Having extra lumens means that you need to flush a lumen that is otherwise not being used.