Yes, you can allow users to sign up with multiple email addresses and use any of them to log in with Ory Kratos. You need to define an identity schema that allows for multiple emails. Here is an example of such a schema:

json {    "$id": "<https://example.com/registration.schema.json>",    "$schema": "<http://json-schema.org/draft-07/schema#>",    "title": "Person",    "type": "object",    "properties": {    "traits": {    "type": "object",    "properties": {    "emails": {    "type": "array",    "items": {    "type": "string",    "format": "email",    "<http://ory.sh/kratos|ory.sh/kratos>": {    "credentials": {    "password": {    "identifier": true    }    }    }    }    }    }    }   }

In this schema, the

emails

field is an array, allowing for multiple email addresses. Each email address is a string in the format of an email, and each can be used as an identifier for the password credential. For more information, you can refer to the [Ory Kratos documentation on customizing identity schemas](https://www.ory.sh/docs/kratos/manage-identities/customize-identity-schema#examples).

In Ory Kratos, you can define a secondary email field in the identity schema to allow users to register with two email addresses. Here is an example of an identity schema with a secondary email address:

json {    "$id": "<https://example.com/ory.schema.json>",    "$schema": "<http://json-schema.org/draft-07/schema#>",    "additionalProperties": false,    "properties": {    "traits": {    "additionalProperties": false,    "properties": {    "email": {    "format": "email",    "<http://ory.sh/kratos|ory.sh/kratos>": {    "credentials": {    "password": {    "identifier": true    },    "webauthn": {    "identifier": true    },    "totp": {    "account_name": true    }    },    "recovery": {    "via": "email"    },    "verification": {    "via": "email"    }    },    "title": "Email address",    "type": "string",    "maxLength": 320    },    "email_secondary": {    "format": "email",    "<http://ory.sh/kratos|ory.sh/kratos>": {    "recovery": {    "via": "email"    },    "verification": {    "via": "email"    }    },    "title": "Email address secondary",    "type": "string",    "maxLength": 320    }    },    "type": "object"    }    },    "title": "Person",    "type": "object"   }

In this schema, both

email

and

email_secondary

fields are defined as recovery addresses. This means that Ory will send recovery messages to both addresses when the recovery flow is initiated. The user should provide the

email_secondary

field during registration or update it later in their account settings so it can be used in the recovery process. For more information, you can refer to the [Ory Kratos documentation on account recovery and password reset](https://www.ory.sh/docs/kratos/self-service/flows/account-recovery-password-reset#fallback-recovery-address).

To associate multiple emails with the same account during registration, you need to customize the identity schema to include an array of emails as shown in the example below:

json {    "$id": "<https://example.com/registration.schema.json>",    "$schema": "<http://json-schema.org/draft-07/schema#>",    "title": "Person",    "type": "object",    "properties": {    "traits": {    "type": "object",    "properties": {    "emails": {    "type": "array",    "items": {    "type": "string",    "format": "email",    "<http://ory.sh/kratos|ory.sh/kratos>": {    "credentials": {    "password": {    "identifier": true    }    }    }    }    }    }    }    }   }

However, the exact API call to register a user with multiple emails depends on your implementation of the registration flow. Ory Kratos does not provide a specific API endpoint for this purpose. Instead, you would typically create a registration form in your application that corresponds to the customized identity schema, and then submit the form data to the Kratos API. For more information, you can refer to the [Ory Kratos documentation on customizing identity schemas](https://www.ory.sh/docs/kratos/manage-identities/customize-identity-schema#examples) and the [Ory Kratos API reference](https://www.ory.sh/docs/kratos/reference/api).

The format you provided does not seem to match the expected format for defining multiple emails in the identity schema for Ory Kratos. The

traits

should be defined in a JSON format, and the

emails

field should be an array of strings, each representing an email address. Here is an example of how you can define multiple emails:

json {   "traits": {     "emails": [       "<mailto:email1@example.com|email1@example.com>",       "<mailto:email2@example.com|email2@example.com>"     ]   } }

In this example,

<mailto:email1@example.com|email1@example.com>

and

<mailto:email2@example.com|email2@example.com>

are the email addresses associated with the account. The user can use any of these emails to log in. For more information, you can refer to the [Ory Kratos documentation on customizing identity schemas](https://www.ory.sh/docs/kratos/manage-identities/customize-identity-schema#examples).

The format you provided does not seem to match the expected format for defining multiple emails in the identity schema for Ory Kratos. The

traits

should be defined in a JSON format, and the

emails

field should be an array of strings, each representing an email address. Here is an example of how you can define multiple emails:

json {{   "traits": {{     "emails": [       "<mailto:email1@example.com|email1@example.com>",       "<mailto:email2@example.com|email2@example.com>"     ]   }} }}

In this example,

<mailto:email1@example.com|email1@example.com>

and

<mailto:email2@example.com|email2@example.com>

are the email addresses associated with the account. The user can use any of these emails to log in. For more information, you can refer to the [Ory Kratos documentation on customizing identity schemas](https://www.ory.sh/docs/kratos/manage-identities/customize-identity-schema#examples).

To adjust the

verification

and

recovery

fields for multiple emails, you would need to define each email in the

traits

section of your identity schema as an object with its own

verification

and

recovery

fields. However, the current version of Ory Kratos does not support this functionality directly. Here's an example of how you might expect to define it:

json {   "traits": {     "emails": [       {         "email": "<mailto:email1@example.com|email1@example.com>",         "<http://ory.sh/kratos|ory.sh/kratos>": {           "verification": {             "via": "email"           },           "recovery": {             "via": "email"           }         }       },       {         "email": "<mailto:email2@example.com|email2@example.com>",         "<http://ory.sh/kratos|ory.sh/kratos>": {           "verification": {             "via": "email"           },           "recovery": {             "via": "email"           }         }       }     ]   } }

However, please note that this is a hypothetical example and may not work with the current version of Ory Kratos. As of now, Ory Kratos expects a single email field for verification and recovery. For more information, you can refer to the [Ory Kratos documentation on identity schemas](https://www.ory.sh/docs/kratos/manage-identities/identity-schema).