Loyalty programs intentionally make it impossible for companies themselves to accrue points, accruing them only to the traveler. Travel departments are aware that travelers want to accrue points, and they generally aren't hostile to it.
Hotels are a tiny bit tricky, but you could try to tell your contact that you prefer, where possible, to stay in a certain chain, and pick one with broader rather than lesser coverage (i.e. Starwood rather than Hyatt). You can also let them know that you are fine with cheaper hotels, say Marriott Courtyard rather than full-service Marriott.
For flights, before going on a trip, you might explore flight options yourself and nudge the travel department. They are usually not getting any better rates than you can get on your own, although they may sometimes have volume deals of one sort or another. But if you know they have preferred arrangements with (say) Southwest, Delta, and USAir, you might pull up the fares for a trip you want to take and if you find a flight you want and it's within a few dollars of the cheapest, tell them you want to take it. Travel departments aren't usually totally in the dark here. If the cheapest flight is $300 and there is another for $340, but the cheapest gets in at 12:10AM and the $340 flight gets in at 8:00, they are usually not going to expect you to get to your hotel at 1AM with an 8:30 meeting, just to save $40. Likewise, if a nonstop is more expensive, they will usually be flexible about spending more to let you have a 3-hour trip rather than a 5-hour trip.
The travel department usually doesn't mind the help. I used to travel frequently, working for small companies with no travel department, and would book my own travel. Now I work for a very large company and travel infrequently, but I've never had them object to a flight I chose. As for hotels, I actually had to harrangue them to let me book "Name Your Own Price" on Priceline. They were reluctant to give up the 10% commission they get as a travel agency, until I showed them that using their hotels I was paying $150 a night, while on Priceline I could be paying $60 or $70.
But if you show them a flight you want, and the price is reasonable, they will usually be happy to book you on that. And nobody will care that you are trying to optimize your loyalty points. Who is going to object, you boss? He's doing the same thing, for sure!!!