You can scale the effect of all targets on the base by editing the Envelope channel or attribute.

Though the slider Envelope only specifies values from 0 to 1, you can enter values from -2 to 2. If Envelope is 2, the influence of every target is doubled. If Envelope is 0.5, the influence of every target is halved. If Envelope is negative, the influence of every target is inverted. If the cumulative effect of the targets deforms the base more than you want, you can scale down the overall deformation effect by setting Envelope to some value between 0 and 1.

For more information on setting the Envelope channel or attribute, see To edit Blend Shape channels with the Channel Box and To edit Blend Shape attributes with the Attribute Editor.