Retirement tax questions

I purchased some annuities way back in 1981 and over the years rolled them over with 1035 exchanges into new annuities with different companies. The current company does not have the correct basis in their record which is higher than what they show. Some of the original companies are no longer there so old records there do not exist. I do have my own records. 

When I withdraw funds from the annuity the basis they will show in the 1099 will be too low. 

How can I claim a higher basis than what the 1099 will show without getting audited?

Thanks,

JM