Inducibility of expression is a function of the promoter of the gene. By genetic manipulation, you can replace a constitutive promoter with an inducible promoter.

Adam is absolutely right. If you express the gene of your interest under a constitutive promoter the enzyme for which it is encoding would be expressed constitutively and will change from inducible to non-inducible.

Thank you for your insight.

By the way I am thinking, is there any probability the enzyme posttranslational interaction?

For example: COX-1 enzyme (if I am not mistaken i is considered as a constitutive enzyme)

Let's say I am interested to increase the production of prostanoids under COX-2 independent condition. I add substance A included coenzyme B and the concentration of interest is obtained. 

Is it possible to have such approach beside manipulating the gene?