It sounds like you need to read PP
How can you increase both your bench press and press on the Texas Method? I don't think doing 5x5 bench, light press, heavy bench one week; and then 5x5 press, light bench, heavy press the next week would train either often enough to get stronger.
Is it better to focus on one lift at a time? If so, how do you at least maintain the other?
It sounds like you need to read PP
Which pages? I have the first edition. Don't remember reading about this...
I would start at p. 179 which details how TM works. You may want to read a little before which explains the needs of an intermediate lifter.
I have the book and I think is not very clear what to do if you want to train the press and the bench.
According to the general principle of the TM one should be able to keep progressing on both lifts as the OP suggested as long as there are volume, recovery and intensity days.
But why was the push press chosen in the example? I wish there was a clear explanation in the book. Because it more closely resembles the press and it can help it more than the bench does? Can the bench press be used instead?
My intuition tells me that at this point of one's training the bench press stimulus would no longer be appropriate for helping the press and vice versa as it was the case for the novice. The movements need to be more specific, hence press and push press can be combined, but bench press, can only be helped with more bench pressing albeit with different parameters: set/weight/speed sets, etc.
The example you are referring to is just one option. I alternate bench and press on TM and I have had good gains on both.
no, it works. Just try it.
In my opinion there are three proven/viable thought processes:
1. Alternate the Bench/Press each week
2. Alternate the Bench/Press each week with the recovery day being the other lift (Bench/Press/Bench, Press/Bench/Press)
3. Bench on Volume and Intensity days, and Press on recovery day with linear loading at 3x5. The bench work alone will be enough to further the press.
Just my opinion but there are countless examples of people using and/all of those options and seeing progress.
-Hat
There's a fourth one. Push Press on volume Day, Press on recovery day, and Bench Press on intensity day. The bench puts the most stress on the pressing muscles because it uses the most weight and more muscle mass to actively move the weight, so it goes on the high intensity day; the push press is less stressful than the bench, so it goes on the moderate intensity day; and the press is the least stressful, so it goes on recovery day.