If they're the same UY and membership number, no. I know that seems a little strange, but it is what it is. For example, we have one membership number with one contract at BLT and one at BWV, both with Feb UYs. But we have another contract with an August UY and membership number at BWV. We can transfer in or out of both memberships once per use year. If we transfer points from one membership number to another, MS generally doesn't count it as one of our transfers.
What I didn't realize and what really surprised me was that you can transfer points twice in one year as long as they're from different use years. For example, this month I transferred 2013 points in to our Feb. UY contract from another member and then transferred 2014 points into the same account, just a few weeks apart.
I had no idea we could do this! I didn't even know members could transfer points from their next UY without borrowing them. I was prepared to transfer them into the August account, but they're Feb. points, so this helps keep everything straight.
And they show up when I sign into the membership site!
Although it's more complicated to keep 2 UYs straight, having two memberships to transfer into is a huge advantage for people like us, who are always point-poor. We're considering buying more points, but at our ages -- 67 and 62-- we'd have to use them for around 10 years to reach the break-even point, factoring in yearly MF.
We're not sure we'll be going to Disney this much in 10 years, plus our grandkids will be much older and probably not interested in going as much either.