by Maurice Y. Michaud (he/him)
From the beginning of Confederation in 1867 until about 1874, a politician could sit simultaneously in his provincial legislature and the federal parliament in what was known as the "double mandate." The man portrayed on this page, Ontario Liberal Edward Blake, took this to an extreme: for a few months in 1871–72, he was the premier of Ontario as well as the member of Parliament for Durham West. So did Pierre-Joseph-Olivier Chauveau, who was premier of Québec and the MP for Québec County from the beginning of Confederation until his resignation from both seats in early 1873, as well as Amor De Cosmos, who sat federally for Victoria while being the premier of British Columbia in 1873. But by the time that Wilfrid Laurier wanted to make the jump to federal politics, he first had to resign from his seat of Drummond-Arthabaska in the Québec legislative assembly, as the double mandate had been abolished.
That being said, a politician who was uncertain of his chances of winning a seat in a general election could run in more than one riding, in case he might lose in his usual riding. The ultimate case of someone doing that was in 1878, when John A. Macdonald ran in Kingston, Marquette, and Victoria (British Columbia). His premonition was right because he lost his usual seat of Kingston, but won both Marquette and Victoria. He kept the latter and resigned from the former which he had won by acclamation, which is what people did when that happened... except Laurier who, from 1911 to 1917, kept the two seats he had won: Quebec East (won by acclamation) and Soulanges. It is unclear why he was allowed to do that, although being the incumbent prime minister may have given him some privilege, or no other Liberal was willing or able to represent the riding.
Meanwhile, nothing prevented someone (particularly in Québec) from sitting in the provincial assembly while being a municipal councillor or mayor. We can think of Simon-Napoléon Parent, who was Québec's premier while being mayor of Québec City at the turn of the last century; Conservative MLA Camillien Houde in Montréal—Sainte-Marie while mayor of Montreal, or even Maurice Tessier who was both Liberal MNA and mayor of Rimouski in the late 1960s. These are just a few examples out of hundreds, but since municipal politics is not covered by PoliCan and the practice has ceased everywhere by the early 1980s, I'm afraid it's up to you to find all the others.
So here is the list of the men who exercised a double mandate in the sense understood in the 19th century. Double mandates were never allowed in New Brunswick, Nova Scotia, and Prince Edward Island; they were abolished in Ontario in 1872; in Manitoba and British Columbia in 1873, and in Québec in 1874. There were 35 in all before they were abolished, most of them in Québec:
I recommend that you read this excellent article (French only) on the website of the National Assembly of Quebec which defines the dual mandate very well and presents the arguments for and against this practice.