Yes, cyanine dyes can be used in tandem with other dyes, resulting in what is more commonly known as ‘tandem dyes’. A tandem dye is made up of two covalently linked fluorescent molecules or fluorophores.  One fluorophore acts as the donor and the other acts as an acceptor.
A donor molecule could be either a protein-based dye such as Phycoerythrin (PE) or Allophycocyanin (APC), or it could be a chemically synthesized dye with a large extinction coefficient.
An acceptor molecule is generally a synthetic dye that absorbs energy emitted by the donor molecule, forming an effective FRET pair with the donor. Cy5 and Cy7 are the most well-known acceptor molecules. Examples of cyanine-based tandem dyes include PE-Cy5.5, APC-Cy5.5, PE-Cy7, and APC-Cy7.