Adding DateFormat into param

func run<T: Decodable>(_ request: URLRequest, _ decoder: JSONDecoder = JSONDecoder(), dateFormat: String? = nil) -> AnyPublisher<Response<T>, Error> {
    return URLSession.shared
        .dataTaskPublisher(for: request)
        .receive(on: DispatchQueue.main)
        .tryMap { result -> Response<T> in
            self.dateFormatter.dateFormat = dateFormat ?? "yyyy-MM-dd'T'HH:mm:ss"
            decoder.dateDecodingStrategy = .formatted(self.dateFormatter)
            let value = try decoder.decode(T.self, from: result.data)
            return Response(value: value, response: result.response)
        }
        .eraseToAnyPublisher()
}
---

Same idea, but with better handle: using a enum which will have "safe values"
enum CustomDateFormat: String {
    case format1 =  "yyyy-MM-dd'T'HH:mm:ss"
    case format2 =  "yyyy-MM-dd'T'HH:mm:ssZ"
}

func run<T: Decodable>(_ request: URLRequest, _ decoder: JSONDecoder = JSONDecoder(), dateFormat: CustomDateFormat = .format1) -> AnyPublisher<Response<T>, Error> {
    return URLSession.shared
        .dataTaskPublisher(for: request)
        .receive(on: DispatchQueue.main)
        .tryMap { result -> Response<T> in
            self.dateFormatter.dateFormat = dateFormat.rawValue
            decoder.dateDecodingStrategy = .formatted(self.dateFormatter)
            let value = try decoder.decode(T.self, from: result.data)
            return Response(value: value, response: result.response)
        }
        .eraseToAnyPublisher()
}

----

//Extension to avoid self.dateFormatter which I guess isn't use elsewhere
// Can be used as private static of your class if needed
extension DateFormatter {

    static var formatter1: DateFormatter {
    //... with Format1
    }
   static var formatter2: DateFormatter {
    //... with Format2
    }
}

func run<T: Decodable>(_ request: URLRequest, _ decoder: JSONDecoder = JSONDecoder(), dateFormatter: DateFormatter = .formatter1) -> AnyPublisher<Response<T>, Error> {
    return URLSession.shared
        .dataTaskPublisher(for: request)
        .receive(on: DispatchQueue.main)
        .tryMap { result -> Response<T> in
            decoder.dateDecodingStrategy = .formatted(dateFormatter)
            let value = try decoder.decode(T.self, from: result.data)
            return Response(value: value, response: result.response)
        }
        .eraseToAnyPublisher()
}

----

//Instead, use the correct JSONDecoder parameter in your current code.
extension JSONDecoder {
    static var defaultDecoder: JSONDecoder {
        let decoder = JSONDecoder()
        let dateFormatter = //Create/retrieve DateFormatter format1
        decoder.dateDecodingStrategy = .formatted(dateFormatter)
    }
    static var otherDecoder: JSONDecoder {
        let decoder = JSONDecoder()
        let dateFormatter = //Create/retrieve DateFormatter format2
        decoder.dateDecodingStrategy = .formatted(dateFormatter)
    }
}

with

func run<T: Decodable>(_ request: URLRequest, _ decoder: JSONDecoder = JSONDecoder()) -> AnyPublisher<Response<T>, Error> {
    return URLSession.shared
        .dataTaskPublisher(for: request)
        .receive(on: DispatchQueue.main)
        .tryMap { result -> Response<T> in
            let value = try decoder.decode(T.self, from: result.data)
            return Response(value: value, response: result.response)
        }
        .eraseToAnyPublisher()
}