Many software systems today face uncertain operating conditions, such as sudden changes in the availability of resources or unexpected user behavior. Without proper mitigation these uncertainties can jeopardize the system goals. Self-adaptation is a common approach to tackle such uncertainties. When the system goals may be compromised, the self-adaptive system has to select the best adaptation option to reconfigure by analyzing the possible adaptation options, i.e., the adaptation space. Yet, analyzing large adaptation spaces using rigorous methods can be resource- and time-consuming, or even be infeasible. One approach to tackle this problem is by using online machine learning to reduce adaptation spaces. However, existing approaches require domain expertise to perform feature engineering to define the learner, and support online adaptation space reduction only for specific goals. To tackle these limitations, we present 'Deep Learning for Adaptation Space Reduction Plus' -- DLASeR+ in short. DLASeR+ offers an extendable learning framework for online adaptation space reduction that does not require feature engineering, while supporting three common types of adaptation goals: threshold, optimization, and set-point goals. We evaluate DLASeR+ on two instances of an Internet-of-Things application with increasing sizes of adaptation spaces for different combinations of adaptation goals. We compare DLASeR+ with a baseline that applies exhaustive analysis and two state-of-the-art approaches for adaptation space reduction that rely on learning. Results show that DLASeR+ is effective with a negligible effect on the realization of the adaptation goals compared to an exhaustive analysis approach, and supports three common types of adaptation goals beyond the state-of-the-art approaches.