Hello,
I'm going to install a 2nd vent stack, but I don't know how close they can be one to another, by code, and to the chimney. Thanks.

I am not aware of any limitations in this situation. Just put it far away from other vent stack, chimneys, valleys, ridges and/or crickets so you can install new flushing and still have enough area left for sealing it with roof tiles or shingles.

Of course, if you have skylight close by, you have to maintain certain distances. In my area it is ten feet.

Hello,
I'm going to install a 2nd vent stack, but I don't know how close they can be one to another, by code, and to the chimney. Thanks.

If you're concerned with keeping in code you better go back and vent both the tubs and lavatories. As for the roof vents, they have no set distance that they have to be separated. Good luck, Tom