Owing Federal Taxes every year

My wife and I both choose Married Filing Jointly on W4 and zero dependents/credits (Despite having two kids).  I also withhold several hundred extra dollars per paycheck to try and avoid a tax bill at years end.  We file taxes as Married filing jointly.  We still owe thousands of dollars each year.   In general, what could we potentially change on W4 or tax filing status to avoid owing every year, less just withholding even more from my paycheck each month?  Would changing W4 as Married filing separately potentially make things better or worse?