The multiple Time-Series design simply adds an equivalent control group to the Time Series design. This provides some information about what might have happened to your experimental group had the experimental treatment not been applied. Since naturally-occurring groups are used instead of randomization, you have less confidence in the equivalence of the two groups; still, the addition of the control group does add some credibility to any positive results by helping to rule out potential rival explanations based on extraneous factors.
Return to quasi-experimental designs.