There is now a third (and last) preprint in our series on multiple categories: M. Grandis - R. Paré Adjoints for multiple categories (On weak and lax multiple categories, III). Preprint: Pubbl. Mat. Univ. Genova, Preprint 606 (2016). Available at: http://www.dima.unige.it/~grandis/Mlc3.pdf Abstract. Continuing our first two papers in this series, we study adjoints for infinite-dimensional multiple categories. The general setting is chiral multiple categories - a weak, partially lax form with directed interchanges between the weak composition laws. The first two papers are: - An introduction to multiple categories (On weak and lax multiple categories, I) Cah. Topol. Géom. Différ. Catég., to appear. - Limits in multiple categories (On weak and lax multiple categories, II) Cah. Topol. Géom. Différ. Catég., to appear. Marco Grandis and Bob Paré [For admin and other information see: http://www.mta.ca/~cat-dist/ ]