Ask Mr. Smarty Plants

Mr. Smarty Plants can relate to your concern! I had the same problem in Central Texas in a native planting in which I left some frogfruit (Phyla nodiflora) already growing there to form a sort of background to the larger plants. With the spring rains, it started taking over and remained aggressive through the summer. It's pretty and is a favorite of many pollinators so I didn't want to eliminate it, but how to keep it from smothering other plants?

The Wasowskis' book Native Texas Plants: Landscaping Region by Region says that it doesn't like to be mowed, taking a long time to recover, so I cut mine back severely, hoping that it would have the same effect as mowing. I also removed colonies of it that were too close to easily-bullied plants. I probably reduced my population by half. Cutting and selective removal seemed to do the trick. The remaining plants still sent out runners, but not nearly as aggressively as before, and enough healthy frogfruit was left to continue to draw lots of small pollinators and provide a background carpet for the taller plants.

Since southeast Texas gets a lot more rain than central Texas, and frogfruit thrives on heavy moisture, what worked for me may not work for you. Your region also has two additional species of frogfruit that may respond differently than the single species we have here (Phyla fruticosa and Phyla lanceolata). If you'd like a low-growing native background plant that isn't quite as aggressive, you might try Straggler Daisy (Calyptocarpus vialis) and/or Carolina Ponyfoot (Dichondra carolinensis), both of whch you likely already have growing naturally nearby if you've got frogfruit. The former is still quite aggressive but less so than frogfruit, and the latter is very low-growing and unlikely to overwhelm anything. Both combine pleasingly with frogfruit.

Phyla nodiflora

Calyptocarpus vialis

Dichondra carolinensis