No. You never edit the EPS itself. The figures it reports come from the employer's tax period, which you can write to at PUT .../tax-period/{tax_year}/{id}/.
Which figures can I set?
cis_deductions_suffered; the statutory pay NIC compensation fields (smp_nic_compensation and its equivalents for the other statutory payments); apprenticeship_levy together with use_apprenticeship_levy_amount_override; ytd_adjustment for year-to-date corrections; employment_allowance_claim; and amount_due_previous_periods and amount_paid_previous_periods. The amount due recalculates straight away. As with every update in the API, PUT replaces the whole record, so send all the fields you want to keep.
What if Employment Allowance was already used with our previous provider?
Set employment_allowance_max_claim on the employer to what remains for the tax year rather than the full annual allowance. Only the balance is then claimed from here on. In the app, the same setting is under Settings > HMRC / RTI.