The Met Office has a yellow “be aware” alert in place for the south west of the country, the Lothians, Borders and Strathclyde areas on Saturday.
The warning, which is in force until just before midnight, highlights further heavy and persistent rainfall throughout the day, with the possibility of more flooding.
The latest advisories come after a day of very wet weather on Friday.
Forecasters warn that homes and businesses could be flooded, causing damage to some buildings, while there is a chance of power cuts and loss of other services to some places.
They add: “Fast flowing or deep floodwater is possible, causing a danger to life.”
The Met Office warning continues: “Following Storm Callum, heavy rain will continue to affect parts of Wales and northwest England along with southern Scotland for much of Saturday.
“Areas of high ground exposed to the south and south west will be most affected, with the potential for a further 20-40 mm quite widely over hills.
“Further strong winds may bring down leaves and branches, increasing the likelihood of flooding due to blocked drains or culverts. The winds should ease later today.”
The Scottish Environment Protection Agency (Sepa) has issued two flood warnings, for the Upper Tay and Ballinluig to Logierait in Tayside.
An earlier warning for the Churchill Barriers in Orkney is no longer in place.
Two flood alerts still exist, for Dumfries and Galloway and the Borders.
On the transport network, some rail services were hit by delays, with the weather affecting the route between Preston and Scotland.
Strong winds have also seen speed restrictions imposed on many routes - with reduced Virgin services between London Euston, Birmingham New Street, and Edinburgh and Glasgow, Network Rail said.
Traffic Scotland has urged motorists to drive with caution due to surface water on the roads.
Sepa’s duty flooding manager David Faichney told BBC Radio Scotland that the band of rain following Storm Callum could bring downpours of more than 30mm.
“Rivers are likely to rise today,” he said.
“I think there will be a lot of surface water. At this time of year, with leaves coming off the trees, drains tend to get blocked up... Flooding of roads, that will happen locally.”
Meanwhile, fresh landslips on Friday caused by Storm Callum as it swept the west of Scotland will keep the Rest and be Thankful closed over the weekend.
Heavy rain and strong winds brought 300 tonnes of debris from the hillside on to the A83 in Argyll and Bute on Friday as operators tried to clear landslips from earlier in the week.
The closure has caused a diversion of almost 60 miles for motorists.
Bear Scotland said work is continuing to repair the debris fencing, clear the carriageway and reinstate drainage.
North west manager Eddie Ross said: “Storm Callum is continuing to bring more heavy rain to the area, limiting visibility and making conditions difficult for the teams to progress repairs and the clear-up of yesterday’s additional landslides.
“Despite this, teams are working exceptionally hard to do all they can to make the area safe, however until then the road and the Old Military Road local diversion has to remain closed for safety reasons.
“We’re aware of the impact this is having on the busy weekend and holiday traffic and we’re doing all we can to help ensure the diversion route via the A85 at Dalmally keeps moving by having further safety patrols on the route to help any motorists as required.”