ばかりか

ばかりか means "not only… but even": the first thing is already a lot, and the second goes further. It follows a noun directly, the plain form of a verb or an い-adjective, or a な-adjective with な. The second half usually carries も, or まで or さえ when the added thing is surprising.

With a negative in the first half, it reads "not only didn't…, but even…".

Requests and plans

ばかりか reports what is the case. The second half cannot be an order, a request or an invitation; use だけでなく there.

• × 英語ばかりか、フランス語も勉強しなさい → 英語だけでなく、フランス語も勉強しなさい

ばかりか, ばかりでなく and だけでなく

All three mean "not only… but also". だけでなく is the everyday one. ばかりでなく is a little more formal and simply adds one thing to another. ばかりか is the most emphatic and the most written: it signals that the second thing is the bigger surprise.