Bench drill with cross feed, morse attaching?

[TexBuxer]

I have old big bench drill and some milling bits. How can I make sure that bit holder stays in place. It has morse cone 2 or 3, and drill chuck drops when adding sideways pressure. I would't like to make permanent modifications.

Edit, so it seem wise not to mill with it. But sometimes there is urgent need to make some tool/part.