It is normally easier and more precise to steer (move and point) the light beam from a light source or an alignment telescope, rather than trying to move a heavy piece of equipment. Some light sources are pretty heavy and cumbersome to move. Most alignment scopes are heavy too. You may have a special adjustable mount for your alignment scope, but perhaps you do not own one. If you do, you’ll notice that they are really heavy too, and they are really expensive to purchase!
Mount your source of light or your alignment scope in a manner which will keep it motionless. Sometimes a Vee-block works fine; and you can even use a wooden Vee-block if you do not have a good metal machinist’s version. Clamp it down, if you can. Watch out for vibration! Anything can induce vibration, including local air conditioning (HVAC) equipment, fans, computers, motors, even persons walking on the wrong kind of floor. Even if you have a metal optical breadboard table, they can vibrate if they are not supported on good, air bladder isolation legs! Vibration of optics can spoil your day.
Then, use mirrors in good tip/tilt and translation mounts to steer the beam the way you need to, to get that beam to your intended destination. The light beam or your optical line of sight (LOS) from an alignment telescope or autocollimator will be easier to control, and get it aligned to your in-line targets and final destination, and you will usually do it in less time, then by trying to move the source or the destination equipment! If you’re steering a narrow laser beam, you can buy beam steering equipment from optics supply firms, usually for a reasonable price. But these tend to have small diameter mirrors, so they may not work for a large diameter beam, such as from an alignment scope.
If you’re using a large diameter beam (like 2 to 4 inches) you may have to implement your own steering mirrors, using the appropriate sized mirrors and good mirror mounts which can support them. Several optics and opto-mechanical supply firms offer good quality mounts. The larger and heavy duty mounts can be over $1,000. each. They are worth it. Do not try to save money by buying flimsy adjustable mounts for these. You will only suffer later on, when mirrors sag and move! Good luck!