Pretty much any stock can be traded on the BATS exchange. Orders can be routed there just like any other exchange.
As far as stocks listed on BATS, it's a short list:
EDEN iShares MSCI Denmark Capped ETF
EFNL iShares MSCI Finland Capped ETF
EMHY iShares Emerging Markets High Yield Bond ETF
EMSH ProShares Short Term USD Emerging Markets Bond ETF
ENOR iShares MSCI Norway Capped ETF
EWAS iShares MSCI Australia Small-Cap ETF
EWCS iShares MSCI Canada Small-Cap ETF
EWGS iShares MSCI Germany Small-Cap ETF
EWUS iShares MSCI United Kingdom Small-Cap ETF
GHYG iShares Global High Yield Corporate Bond ETF
HYHG ProShares High Yield-Interest Rate Hedged ETF
HYXU iShares Global ex USD High Yield Corporate Bond ETF
ICSH iShares Liquidity Income ETF
IGHG ProShares Investment Grade-Interest Rate Hedged
INDA iShares MSCI India ETF
IYLD iShares Morningstar Multi-Asset Income ETF
MRGR ProShares Merger ETF
NEAR iShares Short Maturity Bond ETF
PEX ProShares Global Listed Private Equity ETF
QLTB iShares Baa - Ba Rated Corporate Bond ETF
QLTC iShares B - Ca Rated Corporate Bond ETF
SMIN iShares MSCI India Small-Cap ETF
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