Eurdollars are extremely liquid, but have a pathetically low volatility.
With your 200MM account, a reasonable risk of, say, 1 to 4 % per trade would have you risking 2MM - 8MM dollars. Trading a 4000 - 8000 ES contracts (well below position limits) would achieve that, with a 10pt stop -- and you would have very little trouble entering or exiting your position.
A similar scenario would apply to T Notes, Eurostox and Eurobunds.
Combining all three products, you could EASILY trade your 200MM account as if it were 2MM.
(Now, as for doubling it -- you'll need a bit of skil)