Simple answer Yes, Complex answer see below
You love you mother and your father (likely grandparents, siblings, etc) and if you have children, bet you love them all...
Now Complex answer.
Loving more then one partner reaches two main bumps in my opinion.
1) Our present society tends to discourage not/recognize, so folks are programmed to believe they can only love 'a person', that loving another somehow takes away from the first.
2) True solid 'love' would survive multiple relationships, however, Romantic involvement may not. If you 'LOVE' the person you want them to be happy, whether that is in your arms, or or some one elses arms. Now if you love BEING WITH the person, then you may resent them being with another.
Now for most it is some kind of combination of the two... You love the person (but you also love being with them), so while you may want them to be happy (and a part of you IS happy they can enjoy life with another), there is also a side that is jealous/envious of them.
It can be hard at time, but ask yourself this...
If you Love X.... you want them to be as happy as possible, so if they are truly happier spending time with Y, shouldn't you be happy for them...
Now isn't it even better if they are truly happy spending tme with Y and STILL want to spend time with you and try to make you happy also.