Go ahead if it floats your boat
You can do anything you want. You are a free-willed being. As Jean-Paul Sartre notes, you are in fact condemned to freedom, and the responsibility that unavoidably comes with it. However, Sartre also insists that "freedom itself is not free. We are compelled to act freely; there is no way to avoid being free." Modifying the program is your inescapable right.
If you want to do all the Starting Strength exercises in one session, plus curls, plus hitting the heavy bag, and run a marathon on your off-days, that's your call.
But the cost is that you will burn out quicker than if you stuck to the program. Right now it feels fine because you're not yet lifting heavy enough, but with more weight you will hit a wall very, very fast.
The whole point of Starting Strength is to add weight every workout for as long as possible. The lifts are designed to be as maximally heavy while remaining as minimal as possible, so that you can continue to get stronger while maximally delaying the inevitable wall of grueling workouts, failed lifts, and the slogging stupor of under-recovery. Per the program designer's words:
My program is 3x/week barbell training until the strength gains produced by linear progression are exhausted. That's it, the whole program. Adding a bunch of other stuff in, or even adding a little other stuff in makes it NOT MY PROGRAM, because it fundamentally alters your response to the stress. Do what you want, of course, but it won't be my program if you do it your way.
Squatting, benching, deadlifting, chinning, pressing all on the same day will work for a little while. Then it will be too heavy and you will probably have to backtrack and restart your progress. All five lifts is simply too much to recover from once you're lifting significant weight. In fact, I would argue being able to do all five is a sure-fire sign that you're not working close to the edge of your strength, and you need to add weight. (Which is part of the program.)
So you think you're a better coach than Mark Rippetoe?
I don't mean to criticize. I did the same thing in your shoes. But we all need to realize that it's a little strange for someone who is just picking up a barbell to make dramatic changes to a well-worn program. I understand the mentality. Again, I did it too. I'd bet that seventy five percent of people reading Starting Strength have similar thought processes. It's just that experienced coaches and widespread programs are generally better than a total beginner's ideas. For me, I got better results when I followed the program.
Working around the particulars of your schedule is understandable. Modifying or omitting lifts because of an injury or condition is reasonable. But rearranging the lifts to nearly double the workload is neither of these things. It's more akin to doing a totally different program of your own devising.
Furthermore, fundamentally altering a program as a total novice for the sole reason of "enjoyment" is perhaps not the best way to achieve your goals. But I say that because I want to train, not to exercise. Rippetoe talks about this fundamental distinction in his article on T-Nation, The Biggest Training Fallacy of All:
Exercise and training are two different things. Exercise is physical activity for its own sake, a workout done for the effect it produces today, during the workout or right after you're through.
Training is physical activity done with a longer-term goal in mind, the constituent workouts of which are specifically designed to produce that goal. If a program of physical activity isn't designed to get you stronger or faster or better conditioned by producing a specific stress to which a specific desirable adaptation can occur, you don't get to call it training. It's just exercise. For most people, exercise is perfectly adequate – it's certainly better than sitting on your ass channel-surfing.
You have to ask yourself: are you lifting because it's fun, or to achieve a goal? Do you want to fart around in the gym, or are you there to achieve something? If you want to exercise, modify away. Do the exercises that are fun, arrange them for maximum enjoyment. But if you are training, if you are working towards a goal, if you want to get somewhere long-term by picking up the barbell, I recommend being diligent and consistent and sticking as close as possible to the program as written.
It's your choice. You are inevitably burdened with the responsibility of choosing freely.