Is there a way to store a global or project property inside a virtualized service response script?

Not a problem, I really appreciate the chance to help. I love learning, because who knows? I might need to do the same thing down the road.

I have a sample groovy script that might work.

// Assuming you know how to get the data from the mock Request to save.
def propertyValue = "This is a test"

// Gets the project we're working in
def project = context.mockService.project

def testSuite = project.getTestSuiteByName("Test Suite Name")

def testCase = testSuite.getTestCaseByname("Test Case Name")

def testStep = testCasee.getTestStepByName("Test Step Name")

testStep.setPropertyValue("PropertyName", propertyValue)