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Aah ok that is the catch. In that case I agree with Chris that creating a package of just Content Item, Media Items and Templates should work. But you might face issues with digital marketing related stuff etc. I would keep this answer here for others who are looking for similar upgrade option for source Sitecore version below 8.1.
Thanks Tyler but my question is different. Yes I installed using SIF but OOTB CM/CD/PRC/REP doesn't have separate connection string for Collection Search. What all you have is just Collection, Marketing Automation, Marketing Reporting and xDB Reference Data. I want to add a new connection string dedicated for Collection Search to scale out.