I currently have a 1 1/4 hp pump running 5 jets. Is there a maximum pump size that I should use for the number of jets?
I have the opportunity to purchase a 4 hp pump and I am thinking that I may want to add jets at a later date to the tub but I don't want to over size the pump.

Oh no. Don't put that on there. You'll have more leaks than carters got pills.

Besides you'll have to change the suction/discharge pvc pump unions too.

Thanks for the info. I thought that would be the case but wanted to check first.
One more question though, if I were to add a few jets with the existing pump, what would be the best option. A couple of smaller neck jets, or maybe one or two larger ones.
I'll try to post a picture of the existing tub and ask for some input.

Here is a picture.

Up to 8 Jets I'd try to stay with your existing pump (which should be 1hp, not 1 1/4 - you're probably reading the low speed hp as being 1/4). If not enough, then I'd bump it up to 1.5 hp. 10-12 jets, 2 hp, but at that point you'll also have to change pump common to L2 instead of Neutral because it'll need to be a 230v pump.

Thanks, I checked the pump, it is a Hayward power-flo 3 rated 1-1/2 high speed 1/4 low speed already wired for 230V. So it should have no problem running 8 jets in total then?

It always depends on jet size, plumbing configuration, etc... but you can definitely try it. Everyone's mileage will vary.