Setting up ingress to handle forwarding part of path to service

Question

Long story short - i do not even know how to google it so here i am asking question here:

I want ingress to pass to pod only part of a path it recieves from end user in such manner:

request goes on address www.example.com/svc-prefix/path/to/resource, and to pod i want only example-svc.example-ns/path/to/resource/ to be passed to pod so basically i'd like this "/base/" part to be omitted.

That indicates that nginx.ingress.kubernetes.io/rewrite-target: /$2 is not an option here since www.example.com/path/to/resource is already served by another service.

Example ingress resource:

kind: Ingress
metadata:
  annotations:
    meta.helm.sh/release-name: example-svc
    meta.helm.sh/release-namespace: example-ns
  generation: 1
  name: example-svc
  namespace: example-ns
spec:
  ingressClassName: internal
  rules:
  - host: www.example.com
    http:
      paths:
      - backend:
          serviceName: example-svc
          servicePort: http
        path: /base
        pathType: ImplementationSpecific

As i said I do not even know how to formulate this as a proper question, so if somebody even nudges me with proper keyword or documentation reference i'd be gracious.