I kind of did that and it was slightly messy

I had PLAT & GOLD linked to the same MR, and I cancelled PLAT thinking nothing would affect my AMEX MR account. Wrong, it de-linked from my Gold when they tried to make my GOLD card the "Primary" card etc...
In the end, they kind of just reset it - with a manual adjustment of +XXX points and I lost all the MR history (not a big deal)

So be prepared, but no worries as AMEX does keep your backend MR account active regardless and all the phone reps can see that, even if you cannot

so do what Cana2013 suggests
1. Self-refer your first to earn 15K referral bonus
2. make sure your GOLD card is linked to the same AMEX MR account as your Plat
3. THEN cancel the PLAT and hope for the best

Although, it really depends on how many points you have
If it's not a lot, I'd just transfer it out
With AMEX-Aeroplan it'll be 1:1, but one can hope for AMEX-Avios 50% bonus transfer early next year