Have one unit test project that tests multiple projects

I have 3 projects. Call them project A, B and C. Those projects have very similar functionality even though they have nothing to do with each other. By researching on the internet I see people place their unit tests on the project they are working on.

Let me explain why I find it helpful to create one unit test project that test all the projects instead of 3 unit tests projects.

This is the pattern I am using:

    [Test]
    public void TestFoo()
    {
        var filter = SystemType.ProjectA | SystemType.ProjectC; // Need to test this on projectA and ProjectB

        // linuxSystems are the computers where I perform the tests
        var linuxSystems = Globals.LinuxSystemsToTest();

        foreach (var ls in linuxSystems)
        {
            // do not test if flag is not precent
            if (filter.HasFlag(ls.SystemType) == false)
                return;

            ls.Connect();

            var output = ls.RunCommand("sudo cat /var/someFile");

            Assert.IsTrue(output.Contains("foo"));
            // perform test
        }
    }

If I decide to create a Unit Test project per project (having 3) then I will have to create 2 unit tests calling the same base class. Moreover, when adding a new test if I need to test that on all 3 projects I will have to open the 3 projects and add the test on each project instead of just having the line var filet = SystemType.ProjectA | SystemType.ProjectB | SystemType.ProjectC;. Having one project will prevent me from having to do all that.

What will be the best pattern that you guys recommend for testing my 3 projects?