Objects that wash ashore on the island are being scrutinized.
Farther out across the ocean, authorities on other islands -- Mauritius and the Seychelles -- say they are on the lookout for items bobbing in the waves that might be from the lost jetliner.
At the root of all the hunting is a wing component of a Boeing 777 that was found last week by beach cleaners on Reunion, a French overseas department. Officials say they believe it's most likely from Flight 370, the only 777 plane known to have gone missing over water.
The wing part, known as a flaperon, is at a French lab, awaiting expert verification that's due to begin Wednesday. The remnants of a suitcase that were found on Reunion the day after the flaperon have been sent to another lab for analysis.
Investigators seek 'a direct, physical link'
But other than those two items, nothing else found on Reunion is getting serious consideration from investigators as a possible link to MH370.
Since the passenger jet went missing nearly 17 months ago with 239 people aboard, there have been frequent false alarms amid the far-flung efforts to locate it. Objects initially flagged as possible plane debris turned out to be plain old flotsam and jetsam.
Following that pattern, a metal item found Sunday on Reunion -- described by authorities as an "object of interest" -- drew a lot of attention until officials dismissed it as part of a household ladder.
Relatives of those on board have said they want 100% proof that the flaperon is from Flight 370.
"The preference would be to get a direct, physical link between this flaperon and MH370" in order to give "absolute certainty to the families," said Martin Dolan, the head of the Australian agency that's coordinating the underwater search for the aircraft's remains.
"If we can't do that, then obviously, we'll have to find a way of eliminating all other possibilities," Dolan, the chief commissioner of the Australian Transport Safety Bureau, told CNN's "New Day" on Monday.
Lab analyzed Air France wreckage
It's unclear how long the analysis will take at the lab in France, which previously examined wreckage from Air France Flight 447, a passenger jet that went down in the Atlantic Ocean en route from Rio de Janeiro to Paris in 2009.
If the flaperon is confirmed to be from MH370, relatives say it still won't bring them the closure
that the recovery of their loved ones' remains would provide. It's also unlikely to solve the mystery of why the plane flew wildly off course and dropped off radar.
Australian officials, meanwhile, say the wing component won't change the focus of the underwater search they're overseeing on the other side of the Indian Ocean from Reunion.
Part of the plane showing up on the French island would fit with the ocean current models they have been using, they say.
"We haven't seen anything as a result of this find -- even if it were confirmed absolutely to be from MH370 -- that would lead us to change the search area," Dolan said.
Australia: No plans to widen underwater search
While the flaperon has set off a flurry of searching on Reunion and beyond, it appears unlikely to prolong or widen the Australian-led underwater search.
Australian authorities expanded the search zone earlier this year from 60,000 square kilometers to 120,000 square kilometers, an area bigger than the U.S. state of Pennsylvania. Covering all of it is expected to take the search teams well into next year.
But Australia said in June
that "in the absence of credible new information that leads to the identification of a specific location of the aircraft," it won't be expanded any further.
Australian Deputy Prime Minister Warren Truss reiterated that position in an interview with the Wall Street Journal
"The experts are telling us that there is a 97% possibility that it is in that area, and if you move into a wider area there is just too much to be covered for a small chance of finding the aircraft," he said.