The latest saw NHS Orkney's headquarters at Garden House broken into overnight on Tuesday, with property stolen.
The spate of incidents happened within the space of a week.
Police in Kirkwall are appealing for anyone with information to contact them.

The commitment to get rid of Canada's federal first-past-the-post electoral system was one of his primary election promises.
Opposition parties called the move "cynical and jaded".
Trudeau's Liberal government said the move was made because Canadians were undecided about what kind of voting system they would like to have instead.
"It has become evident that the broad support needed for a change of this magnitude, did not exist," said Minister of Democratic Institutions Karina Gould.
It was a major and surprise reversal for the Trudeau government, which has spent months consulting with Canadians on possible changes to how they elect their federal government, from ranked ballots to proportional representation and online or mandatory voting.
The first-past-the-post voting system, which is also used to elect the UK Parliament, tends to favour larger established parties. Under the system, whoever has the most votes wins their district, regardless of whether they win a majority.
In 2011, the UK voted against moving to an alternative voting system in a nationwide referendum.
In the 2015 election, the Liberals won a majority of seats in Parliament with just 40% of the vote.
During the campaign, before his party had secured its victory, Trudeau had promised that "2015 will be the last federal election conducted under the first-past-the-post voting system".
The change of heart has been described as "absolute cynicism" by members of the opposition.
"They're fearful of having a voting system that doesn't keep Liberals in power forever more," said NDP MP Nathan Cullen, who was on a cross-party committee charged with investigating what kind of voting system Canadians would prefer.
In December, the committee reported that Canadians want the government get rid of first-past-the-post, but did not recommend a specific system to replace it. The committee was divided on whether a referendum needed to be held in order to change the system.
Minister Gould cited this lack of direction as a sign that there was not broad consensus on the issue.
She also pointed to the results of an online government survey launched in December that was widely ridiculed on social media.
The survey did not ask if people wanted a referendum on electoral reform, and people accused it of being misleading and confusing.
"We took the time, we consulted and we listened," Minister Gould said. "There isn't a consensus on how to move forward."
Police in Orkney are investigating a spate of break-ins and attempted break-ins in Kirkwall.
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Canadian Prime Minister Justin Trudeau has broken his promise to change the country's voting system.