Ask Mr. Smarty Plants

There are four members of the physostegia genus native to North America, and three native to Ohio: Physostegia virginiana (obedient plant), Physostegia virginiana ssp. praemorsa (obedient plant) and Physostegia virginiana ssp. virginiana (obedient plant). Since the same care requirements would apply to all of them, we'll use Physostegia virginiana (obedient plant) as our example. 

From our Native Plant Database, here are the Growing Conditons for the obedient plant:

Light Requirement: Sun , Part Shade , Shade
Soil Moisture: Moist
Soil Description: Moist, humus-rich soils.
Conditions Comments: Obedient plant receives its name from the characteristic fact that if you manipulate an individual flower back and forth on its axis, it will stay in position you place it. It is wonderfully adaptable, tolerating both drought and poor drainage. Spreads aggressively by stolons, but is easy to pull out and keep in check. Obedient plant is a good nectar source for butterflies. This perennial is easy to establish and maintain. It can become aggressive but the shallow roots are easy to pull out. 

Also from the Native Plant Database, here are Propagation Instructions:

Description: Propagate by division of roots or by seed. Plant seeds in fall or in spring after damp stratification. Clumps that form from spreading stolons can be divided in early spring or late fall.
Seed Collection: Seeds are 1/8, dull-brown nutlets.
Seed Treatment: Damp stratify 3 months at 40 degrees. 

It looks like division of the existing plants will be the easiest, fastest way to propagate your obedient plants. From Fine Gardening, here is an article on 10 Tips on Dividing Perennial Plants.

From our Native Plant Database:

Physostegia virginiana

Physostegia virginiana

Physostegia virginiana

Physostegia virginiana