Lately I have been thinking about what I could do if I had a normal Blood Bowl team that could steal just one type of unit from any other team. This includes the number of those units, so normal Skaven can field 4 Gutter Runners, and any team that steals Gutter Runners can similarly have 4 of them on the roster. What is the best or most interesting thing you could do using this?
The obvious place to start is to pick a team that has glaring, nasty flaws and see if you can prop them up some. Blood Bowl restricts team to having either players with 4 Agility or 4+ Strength, but you don't get both. (Barring a single Big Guy). Adding high Strength players to an already high Strength team probably won't help much because you won't be able to afford them all and by the time you can your team value will be enormous and you will lack Block. You can surely make a better team this way, but not much better.
The real trick is taking a slow team that is awful at football and making it suddenly a terrifying threat for scoring. Gutter Runners are certainly the first unit I thought of stealing because they are maximally fast, have 4 Agility, and you get 4 of them. Dwarves are normally tough and slow but have no quick scoring threats and are unreliable at playing football. A dwarf team with 13 players including 4 Gutter Runners on it can still field 9 brawling type dwarves on defence and bench 2 Gutters and have plenty of punching power if they want, or switch it up and field all 4 Gutters to create some crazy passing plays if they don't have much time to score. That team would be terrifying, because they still have the normal slow cage progression tactic available but you have to break that cage FAST or a Gutter will dash in for a touchdown.
On the other side you have teams like the elves or skaven who are great at scoring and have lots of potential for big plays but they have huge problems with getting pushed around. They also have the struggle that their linemen are fragile and all units need constant replacement. There are a couple ways you could go there - you could grab Chaos Warriors to have 4 copies of 4 Strength and 9 Armour which would solidify their line immensely, or you could use 6 Saurus instead, which provides absurd amounts of Strength, though it is hard to develop all those Saurus due to them being clumsy.
If you want to go totally nuts you could recruit Ogres and get 6 hitters with Strength 5. That is the absolute pinnacle of beatdown but does have the huge issue of cost. At 140k you will only be able to add in 1 Ogre at most to a normal team so it would take a really long time to purchase them all.
When I try to figure out how I would add units to a midrange team like humans I come up short. They would like both Gutter Runners or Sauruses, as they could develop into a real scoring or bashing team depending on the pick, but no configuration is particularly scary. To do something awesome with this setup you really want a team that already has one thing they do really well, not a team that is mediocre at everything.
There are actually some teams out there that would make me consider taking linemen on as my choice. Ogres, for example, are super expensive and you can normally only afford them because they are accompanied by worthless Snotlings. However, if you grabbed Ork Linemen instead of Snotlings your money problems are worse (they cost 50k instead of 20k) but they actually have 3 Strength so the opponents can't just massacre them effortlessly and they still have 3 Agility so they are capable of playing the ball. They can't play the ball *well*, mind, but they can play as well as a Snotling and instead of being made of paper they are tough as nails.
On a team like Lizardmen I would be tempted to grab Dark Elf Linemen as my pick. They are good at playing the ball and have midrange armour so you could play a really serious bashing game with your Sauruses without worrying that every turn one of your squishies is going to die. You might use a pair of Skinks as dirty players or scoring threats potentially (because your elves can throw the ball) but mostly the team would be just Saurus beatdown and elf football.
In any of these configurations the trick is to make sure you don't commit to more cost than you can afford. Dwarves are expensive, for example, so swapping some of them out for Gutter Runners or even Elf Linemen is no problem. You can't just swap out cheap units for expensive ones though, so fixing up teams like Nurgle or Ogres takes more care.
Off all these options I think the dwarves with Gutter Runners scares me the most. They slot in easily because you can just skip out on buying Dwarven Runners at identical cost, and if you want 4 Gutters to start you just drop 1 Troll Slayer and 1 Lineman to start and you are good to go. You have a tremendous beatdown game and a sturdy core of players so when your Gutters die you should have spare cash around to buy new ones. You have a legit quick scoring threat, great caging ability, and a rock solid financial plan.