Two people died in weather-related accidents in Oklahoma and a man died in San Marcos, Texas.
Parts of Texas saw up to 10 inches of rain over a 24-hour period, with more predicted across the region.
There were numerous rescues on May 24 after banks burst, and hundreds of homes were destroyed in central Texas.
Warnings and alerts stretch from Colorado through to Arkansas, Louisiana, Missouri and eastern Kansas.
One of the worst hit rivers was the Blanco in Texas.
At one point it crested at 43ft – some 30ft above the designated flood stage and 7ft higher than the 1929 record.
A flash flood emergency – reserved for the most life-threatening situations – is in effect in the river basin area.
Some 1,000 people nearby were evacuated and parts of the Interstate 35 highway were flooded and closed.
San Marcos emergency management coordinator, Kenneth Bell, said the body of one man had been recovered but had no more details. Three more people are missing.
Kristi Wyatt, communications director for the town, said: “We have people on car tops and rooftops awaiting rescue. People in homes are going to higher levels.”
She said hundreds of people were now in evacuation centers and that floodwaters had washed away five police cars.
Several hundred houses were destroyed in the town of Wimberley.
A tornado hit Houston briefly on May 24, damaging buildings and injuring at least two people.
Warnings of more tornados have been issued for parts of Iowa, Kansas, Missouri and Illinois.
A mandatory evacuation was ordered at Lake Lewis, 50 miles north of Houston, which itself saw high winds bringing down trees and blowing out windows.
The National Weather Service says Oklahoma City already has a new monthly rainfall record for May – at 18.19 inches.
In Colorado, El Paso and Pueblo counties and the city of Sterling were badly affected.
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