Admittedly I have lived on the fringe of society partly out of choice and partly out of necessity and as a result have several 0's in my earning years. I have earned enough to qualify for SS retirement benefits though small. Early in my working career I had several jobs which were under the table, some were voluntary but generally it was a mandatory condition in order to work. A couple of the employers simply cheated and never paid the taxes even though my checks showed the deductions. I am sure that I have none of those cks to prove it although I'm also sure those employers have an IRS record of non payment. I have worked full time since I was 15yr old in mostly physically hard jobs. Only in the last 2yrs have I been working part time. I turn 64 in a month and am still working as a self employed carpenter. I'm sure my days in this line of work are down to the single digits. Is there any way to remove some of those 0's from my work history?
If you mean is there any way to go back and get credit for your past work, the answer is likely no. Even if some of your former employers held Social Security taxes out of your checks, if they failed to properly report your earnings then there's probably nothing you can do at this point to get credit for those earnings unless you have some type of proof. The best type of proof would be W-2 forms, but other types of proof can sometimes be substituted (https://secure.ssa.gov/apps10/poms.nsf/lnx/0301403052).
If you were self-employed and failed to report or underreported your earnings you can file amended tax returns and pay the appropriate self-employment taxes, but the statute of limitations only permits credit to be given for amended returns filed within 3 years 3 months and 15 days after the end of a tax year.