I have an itinerary coming up where i fly domestically (USA). I want a stopover for the day in a city and then go on to my final destination. To do this, it looks like I'll be flying on one ticket (and probably one airline) to the first city and then flying out on another. I realize I'll have to pick up my bags and check them in again on the new flight.

I'm going to be doing some shopping and probably will be picking up something that I'll want to check in as well. Can I add a third item (a bike) to my outbound carrier if I've checked my bags already. Are there any issues with that? Basically I'll be landing on airline A in the morning, checking my bags with the counter of airline B, heading to the city and then returning to the airport, checking in the sports item and flying out.