Nicola Sturgeon said chief medical officers of all four UK nations have been asked to compile a 'concrete' proposal.
The Federation of Small Businesses said the changes are 'shutting the door' on independent firms during their busiest time of year.
The Scottish Government told families to avoid the annual tradition in a bid to stop further spread of coronavirus.
Capacity issues at the Glasgow Lightouse lab mean 64,000 tests need to be rerouted to other locations.
There are 435 new cases in Greater Glasgow and Clyde, 346 in Lanarkshire and 114 in Lothian.
Nicola Sturgeon urged Scots not to visit other people's homes or travel south to watch Saturday's Old Firm clash.
Scots returning from Italy, San Marino and Vatican City must self-isolate from Sunday.
New regulations on face coverings for weddings, civil partnerships and workplace canteens from Friday.
Measures banning household visits and limiting other gatherings to six people will stay in force.
Welsh First Minister Mark Drakeford says new restrictions will come into force at 6pm on Friday.
The First Minister defended the latest restrictions as 'tough but necessary' in the fight against Covid.
Tuesday's figure of 1297 infections is the highest daily total in Scotland on record.
Number of outdoor visitors permitted extended while indoor visits of up to four hours will be allowed.
However the First Minister urged Scots living in hotspot areas to avoid unnecessary travel due to new coronavirus restrictions.
There are 961 new cases of coronavirus in Scotland but no deaths reported in the last 24 hours.
It takes the death toll among confirmed Covid-19 patients to 2538.
Strict new measures will come into effect on Friday for pubs, restaurants and cafes across Scotland.
Licensed premises in five health board areas to shut, and the rest of pubs in Scotland hit with 6pm indoor curfew.
The 775 new cases amount to 12.6% of newly-tested Scots, among the highest percentages recorded.
It takes Covid-19 deaths to ten this week, while 10.8% of newly-tested Scots have tested positive.