In 1984 Karl Lagerfeld started his own label, and from then on presented 2 collections a year as solely Karl Lagerfeld creations. This has continued in spite of all the other collections he creates.
In the late 80's, he took up the design of porcelain for the West German pottery firm Hutchenrehter and has also found time to continue to design for films and the theatre, as well as neckwear and eyewear for all his contracts.
In 1986 he launched an American Sportswear line, a semi-annual collection with an American point of view.
I've always thought that the typical Lagerfeld client would also be a client of Geoffrey Beene, as both labels had a similar Modernist bent, and both designers loved using metallic fabrics/embellishements.