System for Cross-Domain Identity Management (SCIM) REST API in Salesforce can be used to assign multiple Permission Sets to an user.

1. Create a Connected App in Salesforce.

Connected App Callback URL: https://d8c0000015heneaq-dev-ed.my.salesforce.com/services/oauth2/callback

Here, d8c0000015heneaq-dev-ed is my Salesforce Domain.

2. Note down the Consumer Key and Consumer Secret from the Connected App.

3. Get Salesforce Access Token.

Endpoint: https://d8c0000015heneaq-dev-ed.my.salesforce.com/services/oauth2/token

4. Using the access token from step 3, make a call to SCIM REST AP.

Endpoint:https://d8c0000015heneaq-dev-ed.my.salesforce.com/services/scim/v2/Users/0058c000007oEERAA2

Headers:

Body:

{
  "schemas": [
    "urn:ietf:params:scim:api:messages:2.0:PatchOp"
  ],
  "Operations": [
    {
      "op": "add",
      "value": {
        "entitlements": [
          {
            "value": "0PS8c000003LCCG"
          }, 
          {
              "value": "0PS8c000003MwyT"
          }
        ]
      }
    }
  ]
}

Video Reference: