Migrating Traffic ?!

[farm gate]

Hi,

I hope you can help me on understanding this question of mine. I thank you in advance. Here is the situation:

1. I'm currently building a website for a company X with the domain lets say domainDOTsomething
2. Recentely a company Y with good search ranks and statistics for their website offered their website for my aquisition secondDomainDOTsomething

Question: Is it possible, to alocate website/domain Y on my server being and create a subdomain for my new website with domain X and still, keep the traffic and Google rank/optimisation from website Y? Or in order to keep website Y traffic and Optimisation I have to keep it exactly like it is?

Thank you very much for your help. If I can explain it any other way let me know.
Basiclly the goal is to have the new website with the new domain which is mandatory and keep the other one "inside" this new one with all the traffic it generates already.

Thanks