Does my prediction improve when I use more, but worse classifiers?
I would approach the problem as follow:
Start by splitting your dataset into a test dataset and a training dataset. You would then proceed by building a classifier for each antibody (feature) using only the training dataset and then measure the success of your model on some test dataset (using the measure that you care about e.g. accuracy).
Usually you cannot repeat the process I described above for all combination of antibodies (features), due to time constraints. Their is a variety of methods you can consider which can be found if you search for feature selection techniques e.g. wrapper, embedded, filter etc.
Since it sounds like you already have a good idea of which features (antibodies) are important, I would recommend trying forward features selection. The idea is that you start building multiple models using only 1 feature (antibody) and determine which one is the best. Let's refer to these as selected features from now on.
For each unselected feature

Build a model using the selected features and one of the unselected features (in this case we will build a model using your best antibody and one other antibody)
Measure the performance of the model on the test set and store it

Once you are done you check if by adding only one feature did it improve the performance in comparison to using only one antibody. If it did you add the best antibody to your original best antibody, so now your model has two selected features.
You can repeat this process, until the performance starts to drop. The method does not search the whole space, but it still gives some descent results.