It varies from state to state. The best thing you can do is consult with a family law attorney in your childs county - jurisdiction. There are tendencies with each area...of course there are state statutes too, but then inside that you have judges who tend to rule a certain way - a experienced attorney can advice you of this for your area.
I want to think it being NYC as being somewhat more liberal and having a couple days every week...you have that...I would HOPE a judge would not take away existing time...that is confusing to the kid. You can always request the status quo...and request a graduated visitation plan leading towards shared parenting. That is a common request. Ask for mid-week visits...even if not an overnight...at least 4 hours every Wednesday.
When school starts...if mom fights it you won't keep every weekend as both parents should have weekend time. THEN your graduated plan can reflect you have time with child during the school week, two days/nights - can parent during the school week, and EOW. Some parents do a Thursday visit every week...as child gets older EOW can become Thursday after school to Monday take to school.
Your best bet is consulting with a local attorney, again. That is the only way to see what the trends are.
Joint legal custody is pretty much the norm across the US.
your county family law division will have recommended visitation guidelines for diff. age children. There are also lots of books.