This almost how I'd expect any successful American adaptation of the program during the 90s to look before it's quietly migrated to The CW in the 00s for its underwhelming final two seasons.
The McGann Years
After the 1996 pilot 'movie' - where McGann regenerates from Tom Baker, explicitly seperating from the 'classic' canon - the show settled into a format where the Doctor, Grace, and Chang have adventures in time and space, often clashing with the Master. Of the twenty episodes a year, four needed to be written by British writers and filmed in the UK as part of the BBC's deal with Fox, backed up by McGann who'd quite like to visit his friends and family some time. The Cybermen, the Sontarans, and the Master would be the recurring foes in the first season, while various episodes would be adaptations of original Who stories and Charisma Carpenter made guest appearances as Sarah Jane Smith. S1 ended on a loose remake of the Web of Fear, featuring the Master taking over the New York subway system and featuring Clancy Brown as the cigar-chomping Brigadier Lethbridge.
While S1 had its high points, it had notable flaws: episodes set in the future criticised for being "cod-Sliders", the Cybermen being "too Borg" (and deliberately so), and Chang being a third-wheel comic relief character with no real role. S2-3 changed that (unfortunately this included dropping Chang rather than writing him better) and, after negotiations with the Nation estate, brought in the Daleks and sparked off a mini-Dalekmania. A spinoff about Sara Kingdom (played by Claudia Christian) would get trailed and released most of the way through S3. A version of UNIT, now a paramilitary Men in Black outfit, would be brought in for the present-day Earth stories.
S4 would then run into issues. Daphne Ashbrook had dramatically left the series near the end of S3, and the show plugged the gap by elevating Carpenter to main role (causing bad blood between Doctor Who and the Mutant Enemy team, as it eleventh-houred the plans for Angel), but this removed the will-they-won't-they element between the Doctor and Grace. So the show put it in halfway through S4 with Sarah Jane and it was too awkward a fit. Worse, the show had a money spat with the Nation estate and lost the Daleks; the US-original monsters had yet to catch on; and some of the classic beasties from the show were already in license agreements with outfits like Reeltime, BBV, and Telos Publishing.
McGann, at this point, decided to leave.
The Mayall Year
S5 is popular in Britain and Australia. America, not so much - Rick Mayall was an inspired choice for the Doctor but
not the smouldering handsome romantic lead McGann was, and his portrayal aggressively anarchic and manic. Attempts at will-they-won't-they died a death. Running low on monsters, the show had turned to the Quarks as a really obvious power play with the Nation estate, "we don't NEED Daleks to do Dalek stories", and the critics & fans howled in derision.
Ratings dropped in America but went
up in the UK, so the show got shifted to UPN from this point.
The Wolf Years
Jobbing actor
Matt Wolf had his big break as UPN aimed for a younger, sexier Doctor with equally young, sexy college-ish companions. To save money, the show now focused a lot of the Earth-based stories on Lambert College and tried to negotiate out of the UK filming commitment (it finally would by S7). A deal was made to get the Daleks back.
Ratings stabilised due to the escapades of the hunky Doctor and his companion, at least in America; ratings dipped in the UK, Ireland, and Australia. The show merrily carried on with what one critic called "Who's Buffy" for three years, but by S8 this format was notably tired and stale. It didn't help that the UK-writers mandate had ended by then, removing a source of episodes that were often divergent from the American writer's room.
To boost ratings in S8, the Master made a reappearance (Eric Roberts cost money and so had been left out of UPN) for a five-story arc that ended with Lambert College exploding, the Master finally dead, and the Doctor in a cliffhanger for S9: waking up in a WW2 POW hospital tent to see a Sontaran in a Nazi uniform.
S9 was an ambitious attempt to do a year-long serial, with the Doctor stuck in the 1940s trying to ensure time stayed on track and knowing his new companion, a US Army nurse, was historically doomed to die. The ambition was more than the show could actually pull off with its writers or its budget or with an audience who'd been expecting more variety. With ratings dropping, the fourteenth episode abruptly pivoted into a War Games remake before sending the Doctor back to Modern Day
Canada America with a very hastily introduced new companion. Understandably, Wolf wanted to move on at this point.
The Shephard Years
Character actor Mark Shephard took over as the UPN turned into the CW and the budget was in shambles. He was promised it would just be one year as the show wouldn't move to the CW. He was there for
three years as executives decided Doctor Who was still doing okay enough as long as more cuts were done. This was a problem as not only did Shephard not really
want to do three years, his first year was a continuity-heavy ending that saw a Time War between Daleks and Time Lords and an appearance by Richard E Grant as an alternative universe Doctor (referencing the 'Classic Who' expanded universe).
Nobody knew what the hell they were doing in the last two years. Plotlines meander, the companions are rapidly cycled through because agents wouldn't let their clients be tied down, returning characters pop up (and sometimes die) in desperate attempts to wean actors back, the money wasn't there for returning classic monsters, and the sets wobble. The Master was back from the dead in the Time War as a new actor but
that actor had, thinking Doctor Who was ending, got a recurring role on another show and so could be barely used. Weirdest of all, the show crossed over with Supernatural and thus made demons & ghosts canonical to Who (?).
Mark Shephard became so disgruntled that he contrived to
escape and made enough trouble on set to 'negotiate' an early release.
The Marcell Weeks
Joseph Marcell agreed to do the last four episodes of Doctor Who solely because he'd been in Remembrance of the Daleks and thought it'd be a laugh to get to
be the Doctor after. The atmosphere on set was
not a laugh. In an attempt at tying things off, the Doctor's last scene is being shot by gangsters in a future San Francisco after capturing the Master and he starts to regenerate. All this did was mean the CW had to confirm the show was cancelled, this wasn't a hint it was coming back after all with a new actor.