fx - Cross Currency Swap Pricing in nowadays environment

Multicurve setting has now become the new paradigm for vanilla swap valuation. For the record I give here (without getting into too much details) the methodoloy for pricing Euribor3M swaps in this setting.

Step 1-Get your discounting curve from OIS Swap Curve quotes, by standard bootstrapping method just like in the old days.

Step 2-Using Euribor3M swaps ATM quotes and the OIS discount curve of step 1, bootstrap a "forward" curve of discount factors that can be used to get "adjusted" Euribor3M forward rates such that those "adjusted" forwards discounted over OIS curve gives the Euribor3M ATM Swap quotes (the fixed rate cashflows are discounted with OIS Curve).

(I hope I'm sufficiently clear if not let me know I will add extra explanations)

I was wondering about the corresponding setting (i.e. curve construction) for Cross Currency Swaps (CCY Swaps) products.

Here is a setting for Cross Currency Swaps Euribor3M +Margin vs Libusd3M collateralized in USD (at Fed Fund rate) that I believe is correct. So here it is :

Step 1,2- Construct the USD curves as in Step 1 and Step 2 with Fed Fund Swap Rates and Libusd3M ATM Swaps quotes.

Step 3- Then use Forward FX quotes over USD/EUR currency pair to bootstrap (together with the Fed Fund discounting curve) an $OIS^{usd}$ discount curve thank's to the spot/forward arbitrage argument where the unknowns are of course the $OIS^{usd}$ discount factors.

Step 4- Use Cross Currency ATM Swap Quotes, to build a "$Euribor3M^{usd}$ adjusted" curve using the 3 curves already built (with the spot Eur/USD exchange rate) so that all discounted cashflows (valued in USD) of those CCY ATM Swaps get a zero PV (in USD).

If anyone implied with CCY Swap valuation on a daily basis read this post, I would be grateful if he could confirm/infirm the relevance of this setting.

Best regards

PS 1 : This is not really an option pricing question nevertheless such a setting is the basis for any Multicurve option derivative model for any Cross Curreny Interest Rate Options so it seems important to me to establish first the market practice over underlying instruments before going further.

PS 2 : You can rebuild step 1 to 4 using EUR as collateral (with EONIA rate) then you would shortly discover that ( even if all ATM instruments give the same ATM margin and rates by construction), when pricing OTM or ITM Cross currency swaps you get different Net PVs if you use one setting or the other. This does not entails arbitrage as this difference actually originate from the different collateral settings.

Best regards