public interface ICache
    {
    }

    public abstract class ProcessorBase
    {
        protected ProcessorBase(ICache cache){}

        public abstract void Process();

        protected T GetFromCache<T>()
        {
            //извлекаем из кеша
        }
    }

    public class ProcessorA: ProcessorBase
    {
        public ProcessorA(ICache cache) : base(cache) {}

        public override void Process()
        {
            var data = this.GetFromCache<int>();
            // логика1
        }
    }

    public class ProcessorB : ProcessorBase
    {
        public ProcessorB(ICache cache) : base(cache) { }

        public override void Process()
        {
            var data = this.GetFromCache<string>();
            // логика2
        }
    }