How many PhD students are too many?

This is more of a qualifying remark: What your eventual target might be should probably be different from your current target. Advising students is a skill you have to learn and learning this skill will take time. So I'd recommend starting small until significant parts become routine. Also, more senior students might be able to show new students the ropes, so staggering might be useful too.

There are of course a lot of other constraints, so don't take this as your only criterium.

There’s no right answer here. It really depends on what level of supervision you want to provide. The more direct interaction you want with your group members, the smaller your group must be. The more grant money and support you have, the larger your group must be. If you need your students to assist with teaching duties (e.g., if TA’s are assigned to faculty rather than courses), you may need a larger group than a smaller one. For promotion, you may need to have a certain number of graduates or currently supervised students.

So this leads to groups with just a few students all the way up to groups with scores of graduate students and everything in between.

This depends on many things, such as whether you have tenure, whether you have postdocs or other “in-house” faculty to help you advise and mentor grads, how demanding the students themselves are, how many people you have space/equipment for, how many students you can expect to support financially, and how much time/effort you want to put into advising — both as opposed to your other work and as opposed to your personal life.

In my experience, having observed this for some time, a lone advisor typically accepts no more than two grads. If they have a postdoc or equivalent, they will sometimes accept another grad or two and share the advising with their postdoc.

If you’re going for tenure, obviously focus on that, with guidance from more senior faculty in your department. Expect to successfully mentor a grad or two by the time your tenure review cones up. This shows you are valuable to your institution.

Some grads and research projects are naturally more or less demanding on your time. You’ll need to evaluate how demanding potential grads and/or research projects would be before recruiting any. Allocate slightly more time than you expect, to be safe.

Some groups are constrained by lab equipment and/or space. Competing for time to use special equipment is difficult for grads. You want to make sure you don’t recruit more grads than you have room for.

It’s also difficult for grads to have to look for funding elsewhere, as this takes significant time away from their research. Of course, seeking funding on their own is good experience for them on many levels, but being able to provide funding makes everyone happier. Not being funded can cause grads to take way longer than they should to graduate, which is stressful foe them and you. Consider how much you will be able to help support them financially (e.g. as a Research Assistant) and how likely it is they will be able to secure funding on their own (with your guidance) for their research.

You also need to consider your own plans. Do you have a sabbatical coming up? Will you be working off-site or traveling a significant amount of time over the next few years? Are you going through some demanding personal challenges, such as divorce, mental illness, physical illness, having kids, and so on? If so, you might avoid recruiting new grads unless you or others will be able to support them during these times.

One word of caution: don’t recruit a large group all at once, as doing so has the potential for you to become dangerously overcommitted. Start small and add as you learn what you can handle.