NHS Grampian and NHS Ayrshire and Arran have asked the Scottish Government to put forward a bid for military support, while NHS Greater Glasgow and Clyde said officials were “exploring options” regarding assistance.
It comes after the Scottish Government announced last week that NHS Borders and NHS Lanarkshire had both been granted military help.
The government also confirmed it has asked the Ministry of Defence for assistance with the Covid-19 booster and flu vaccine campaigns.
The requests from Grampian and Ayrshire and Arran are still being considered by the Scottish Government and have not yet been put forward to the MoD.
Health secretary Humza Yousaf said on Monday that the government would consider requests from health boards “favourably”, and “certainly look to make an approach to the military for assistance”.
A spokesperson for the MoD described a “fluid situation” and said the MoD would be willing to provide help, so long as the criteria for Military Aid to the Civil Authorities (MACA) were met.
But they added that military support could not be a substitute for long-term issues.
Soldiers are set to begin working with NHS Borders and Lanarkshire on Tuesday.
A total of 86 personnel deployed at least until November 10, with this date kept under review.
It will be the first time the military will be used to support acute care in NHS Scotland.
Dr Lewis Morrison, Chair of BMA Scotland, said the move “emphasises the seriousness and scale of the pressures on NHS services and frontline healthcare staff”, adding that things are “on a knife edge in the areas where this is happening.”
Head of health intelligence at NHS Grampian, Jilly Evans, said the health board would “welcome” military support.
Asked on Monday if Grampian may need the same measures as the Borders and Lanarkshire, she said: “I think we would welcome that if that were possible for us, and I think many boards will feel the same way.
"Particularly the possibility of nursing staff would be really important to us. We’d back it up and augment it with some fantastic volunteers who help us with transport situations, but having military support would be a real boost to us too.”
A spokesperson for the Scottish Government said the request was being considered.
They said: “The Scottish Government is aware that requests for military assistance have been received from NHS Grampian and NHS Ayrshire and Arran.
"Additionally, we are working with our military colleagues in respect of a request for military vaccinators to support the Seasonal Flu and Covid-19 booster campaign.
“Requests from health boards for assistance are assessed by the Scottish Government, with support from our Military Liaison Officers.
"Where Scottish Ministers have approved a request for support, a formal request for military assistance is then made to the UK Government, firstly through structures in Scotland and thereafter to the MoD.”
Mr Yousaf previously said the Scottish Government would look “favourably” on such requests.
He added: “But you can imagine, the military is getting these requests from every single health board and NHS Trust across the entire United Kingdom.
“So no doubt they are also stretched.”
Other health boards are understood to be considering asking for help.
It is understood that no formal request has yet been made by NHS Greater Glasgow and Clyde, but a spokesperson said the health board “is exploring options regarding assistance from the army.”
Opposition MSPs urged the government to “get on top of” pressures in the NHS, and respond to requests from health boards as quickly as possible.
Scottish Conservative Shadow Health Secretary Sandesh Gulhane said: “Humza Yousaf must now urgently guarantee the support from our military will be maximised at every turn for these health boards, and any others who request it.
“Otherwise he will be the Health Secretary who presides over a truly disastrous winter in our NHS.”
Labour’s Jackie Baillie said it is “abundantly clear” that more military support will be needed over the winter.
"We must thank the British Army for helping the NHS but this is just a short-term sticking plaster,” she said.
“The government must seriously consider asking them to help construct field hospitals, if that is supported by clinical evidence.
“Our NHS is experiencing a winter crisis already due to the SNP’s complete failure to support our health system. There really is no time to waste.”