Can the activity of a specific gene in a cell artficially be increased?
There are technologies available for inducing higher (or lower) gene expression in cultured mammalian/human cells as well as in bacteria. The state of the art is CRISPR-mediated gene activation/repression, where you fuse a transcription activation domain to a Cas gene in a CRISPR-Cas system (usually Cas9), and provide a guide RNA to target genes of interest. This Cas gene is made "nuclease-dead" so that it can only target but not cut or degrade DNA (as opposed to natural CRISPR-Cas systems that do both), and serves to bring the transcription activation domain to your gene of interest, which leads to an increase in transcription of that gene. 

Check out this paper for an earlier example of such a system in cultured cell lines. The field has advanced quite a bit since then, and people have successfully activated genes in mouse lines