Health chiefs have been alerted to a case in Pleck, Walsall, on the border with Sandwell, which partly falls under the same WS2 postcode area where the region's first case of the variant was identified at the end of last month.
A drop and collect testing service in Walsall is set to be extended, while health chiefs in Sandwell say they are ready to launch a similar scheme.
Mass testing of more than 10,000 people is currently underway in WS2 with firefighters drafted in to help with door-to-door testing and mobile testing units set up.
It is understood the latest case was found after a positive test on January 26 and that council chiefs were alerted on February 11.
It was not found through the testing regime in WS2, and is not believed to be linked to international travel.
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Dr Lisa McNally, Sandwell's director of public health, said she was made aware of the new case last night and that plans were in place to ramp up testing.
"I have been made aware that there is a second case and that it is right on the border with Sandwell," she said.
"We have a plan ready to go if we need to set up a drop and collect service. We also have a system in place so that if someone is found with the new variant, they are supported to isolate, so we can call them each day to make sure they have everything they need.
"Obviously the aim is to control that spread so the last thing we would want is for them to be popping out to the shops.
"We are ready to rock and roll as soon as we get the call."
Councillor Mike Bird, the leader of Walsall Council, said: "I am aware that another case has been found. This came to light yesterday. It is not linked to travel and is not linked to the testing regime that we are conducting in WS2.
"What it does mean, is that we will be mobilising our people to go through a similar process to what we have done in WS2 regards testing.
"What we are looking at is a drop and deliver service, so we will drop tests at people's doors and we'll be asking them to return them to a central collection point.
"It is disappointing, but we've had a trial run now and no doubt we can build on what we've done."
Mr Bird said that 85 per cent of around 10,300 people in WS2 had now been offered a test, either through drop and collect or at a mobile testing unit.
A small number of people are said to have declined the offer. Council chiefs are yet to be made aware of any results.
The South African variant is said to be more easily transmissible and its emergence in the region has sparked concerns that infection rates could start to rise again.
A new case was confirmed on Thursday in Stafford, while cases have been identified in the Northfield area of Birmingham and Worcestershire.
Meanwhile one family was left upset when the swab they were sent to test themselves with turned out to have already been used by someone else.