If you have already filed a your taxes and it's pending, then you just can't file another 1040.
If you need to make changes, wait until it's been accepted by the IRS then file an amended 1040, I think it's 1040X.
Check with the IRS web site or call them, they will let you know what to do,if you need to refile.
What would be the purpose?
If you are thinking it is going to get you a refund faster, you are wrong. In fact, it could possibly delay your refund depending on where the current return is at- if they are both submitted at the same time, both could get kicked out. Likely, it would just be a waste of time (and money) because the H&R Block one would probably be accepted first and the Turbo Tax return would be rejected.
Last year, I NEVER received acceptance and I still got the refund exactly when I was told by the IRS to anticipate it- no sooner and no later. Not having that acceptance does not mean it has not been accepted, there seem to be some glitches. Anyone who was accepted by 11 a.m. EST tomorrow will receive their refund at the same time, regardless of who they used to prepare their taxes.