ZOHO Office Integrator is embedded in our website using an iframe. When using Chrome's incognito mode (or Safari browser standard mode) we get next error after first attempt to edit the document: "5022 : Cookies are disable in your browser. Please enable cookies." 

Browser security settings are default: "Block third-party cookies in Incognito"

So for now editor is not working in Safari and Chrome's incognito mode. But Google is intended to drop thrid-party cookies support in the future and this will become bigger problem then.

Is there some solution for this problem except setting up custom domain for Zoho Office Integrator?

Attached browser's console output and update request response.