How does blocking the re-uptake of serotonin increase the amount of serotonin available for neurotransmission?

I understand that SSRIs work by inhibiting the process of recycling serotonin but if the reuptake is blocked does this force the cell to produce more serotonin? If not, it seems like enhancing the reuptake would be the goal so that there would be more of the neurotransmitter available for the next signal. Can any medical professionals help me understand this process?