We will eventually add on an addition to our home. Due to the cost of an addition, we would like to first have a patio poured. Would the contractor be able to set the addition foundation up against this slab? Pouring the slab to the house probably doesn't make sense.
Garrett, pouring the patio first can be done, but great care will need to be taken for everything to work out correctly when the addition is complete. In order to make sure the patio is in the right location, it will almost be necessary that you have the blueprints for the addition drawn. Keep in mind that being even an inch off with the patio can be a problem. An inch too close to the house could affect the addition's roofline and how it ties into your existing home. The same is true if it's an inch too far away from the house.
And just having the blueprints isn't going to be enough - you will also need a concrete contractor with enough experience to be able to read them and get the patio in the correct place. While many concrete contractors may have that expertise, there are also quite a few who don't. It might be a good idea to talk to a general contractor who is qualified to build the addition. Explain that the addition will be a future project that you might consider them for, but you would like the patio to be installed now. They might be willing to pour the patio if they know there's a chance they could be doing the addition and there would be incentive to make sure it's in the correct location.
Also, most concrete slabs used for patios do not have footings at their perimeter - they are pretty much just a slab with gravel underneath for drainage. Some will have rebar in them and others wire mesh to provide a little strength. Your addition, though, will almost surely have a concrete footing at its perimeter. This provides support for the framing of the outside walls that carry much of the weight when building a home or an addition.
I'm not sure what type of floor system your addition will have or if it will be a slab as well, but in many cases, the footing for a structure extends out past the outside dimension of the wall above it. This means it's possible the addition footing could extend underneath your new patio. If you have this situation, the general contractor doing the patio will probably need to dig and pour that section of footing before installing the patio. Rebar should be extended out both ends of the footing so when the remainder is poured as the addition gets underway, it can be tied into the section that has already been poured.
Ideally a structure's footing should be poured all at once, but doing it in sections can be a possibility providing everything is tied together correctly. Your contractor may need to get an engineer involved and the footing will almost definitely need to be inspected by the building inspection office of the local jurisdiction prior to being poured.