The thefts occurred sometime overnight on Monday at separate addresses in Curran Crescent, Cardoss Road and Aitken Orr Drive in Broxburn.
In each case a part of the exhaust system or catalytic converter was stolen, causing between £1000 and £3000 of damage per van.
The incidents mirror 12 thefts which took place across the Capital between December 30 and January 6.
Motorists are being urged to be vigilant against the thieves, who have been focusing on Mercedes exhaust systems as they contain precious metals.
They are composed of several metals, including small amounts of platinum and palladium, making them a target for criminals.
Taxis and commercial vehicles were among those targeted across the Capital – in areas including Morningside, Leith, Oxgangs and Willowbrae.
Mercedes Sprinter vans and Mercedes Vito taxis and vans have been the most popular targets for the thieves.
Livingston-based local authority liaison officer, Sergeant John Jackson, said: “It would appear that this criminal activity has now spread to West Lothian.
“Our inquiries into these reports are ongoing and I would be interested to hear from anyone who has information that can help with the ongoing investigation. Unfortunately, we have seen police forces right across the UK receive similar reports and it’s an offence not specific to Scotland.”
Sgt Jackson said he wanted to reassure drivers that Mercedes cars were not being targeted.
Drivers of commercial vehicles are being urged to take extra precautions, such as parking in an area covered by CCTV or secure lighting.
So-called “defensive parking” – which involves leaving your vehicle in a spot that restricts someone from gaining access to the underside – is also being recommended by officers.
Sgt Jackson added: “It’s also worth considering the purchase of specialist security products that can be fitted to catalytic converters in order to make them more secure.”
Anyone with information is encouraged to contact police on 101 or make an anonymous report to Crimestoppers on 0800 555 111.