You should look at the following link for striping methods of tissues and cells:

https://www.researchgate.net/post/Is_it_possible_to_effectively_strip_and_reprobe_tissues_for_whole_mount_immunofluorescence

Instead of visualization by AEC (red) for the the second labeling, you could try DAB, which gives a brown color.

But still, there is a big issue with your sequential protocol! This visualization system  produces precipitates in the vicinity of the HRP. The more you let the enzyme acts, the more the precipitate diffuses and becomes denser. Will the first precipitate be removed after striping or not? If not it may block the access of your second antibody and HRP to the protein B , and the HRP of the first labeling may be still active, so you will obtain a brown precipitate but corresponding to the HRP of protein A not B.

You should really consider to avoid sequential labeling, by using two different systems like HRP and AP. Here is a PDF file with protocols with such double labeling. Hopefully you will find some inspiration.

If you really want to study precise "colocalization" of your two proteins in cells on coverslips, the best is immunofluorescence with, at least, confocal microscopy, as precipitates give diffused signal that spreads with reaction times.

Unfortunately IF is not an option at this point in time. I do not need to perform any expression quantification, I simply want to view protein expression levels in senesced cells and use a second senescent protein marker in order to confirm co-localization in a way that goes beyond morphology visualization of the cell. 

Verena, I may try this method. However, upon washing off AEC with ethanol, will there likely be some left over HRP secondary from the first primary that will come up when staining for the second species? Is there a concentration of ethanol you may recommend so that I do not damage the samples? Thank you.

Great. Thank you very much, I will try this method.