It could be used as a flexible "tidal flow" lane - citybound in the morning rush of merging traffic from Welcome Bay and State Highway 29A in both directions, then the reverse in the evening, and possibly dedicated to buses or other vehicles with three or more people.
In a meeting on Monday, the city's councillors will receive the results of a second engineering assessment.
Parkes said they found the bridge's piles and deck could cope with extra loading of another lane, and had enough longevity to make the (as yet unknown) cost of improvements likely worthwhile.
He said challenges included designing a clip-on or separated lane for cyclists and pedestrians; cultural and environmental considerations, particularly around the harbour; and timing issues to avoid overlapping the Baypark to Bayfair works due to finish in 2020.
There were also resource consent obstacles, especially to extend the third lane up Turret Rd towards 15th Ave, a sensitive stretch of road with houses on one side and beloved pohutukawa trees on the other.
Parkes said there would be no point adding another lane to the bridge if it could not be continued up Turret Rd.
The council already had plans in place to widen 15th Ave, due to start in February.
Sustainable Business Network Bay of Plenty regional manager Glen Crowther said a third lane could be "a real game-changer" for congestion.
It was a cost-effective option in the short term, but may also work well into the long-term, given the congestion went only one way in the morning and the other way in the evening.
"This is the perfect place to trial something like this in Tauranga".
Commuters received the news with cautious optimism.
Welcome Bay real estate agent Tammy Francis said she drove over the bridge every day about 8.15am on the school run.
The Maungatapu underpass had made a difference but generally, it was "chocka".
A third lane would be "great" but she said the wait would be painful if it was years away.
Two self-employed men - Josh Cole from Poike and Bruce Buchannan from Hairini - said they arranged their days to avoid the bridge during rush hours.
Cole said a third lane was a good idea but worried any gains would be lost within a few years due to population growth.
He wanted to see the council focus on sustainable public transport options such as buses and light rail so the city did not end up like Auckland.
Councillor Bill Grainger said he wanted to work under way within one or two years.
"If we can make anything work on that bridge as it is ... let's do it."