Yes, as catgirl says, you can be an Intersectional Feminist!
I know some have suggested here and elsewhere that this involves a "watering down" of the feminist perspective or diminishing the impact of institutional misogyny, but I disagree.
In my view, it acknowledges the lived experiences of all women - something certainly women of colour, working class women and other women who experience "intersectional oppression" have often criticised the feminist movement for failing to do. Although all women do have some shared experiences, especially of the outcomes of institutional misogyny, we are a diverse group and we don't always understand or even acknowledge the differing experiences of some of our sisters.
Perhaps there is a worry that by acknowledging the ways in which some of us are privileged will diminish the argument that women as a class, all women to some degree, suffer as the result of institutionalised sexism and misogyny. I don't believe that is the case though. And, saying that some women because of their situation are privileged in some ways is not being anti-feminist.
I believe more collaboration with other social justice movements can make our voices stronger, make better use of ours scarce resources and ensure we are always challenging ourselves on inclusivity.
I have positive experiences of working in a feminist organisation, collaborating with other organisations working for social justice on issues including racial equality, against LBGTQ discrimination, against disability discrimination, etc. A few of us would rock up to a decision-making body to challenge their plans and policies. When someone from an LBGTQ organisation spoke up about an issue of gender-based exclusion, then someone from an organisation for older people made a point about racism, it sent a clear message that "divide and rule" tactics wouldn't wash.
This kind of collaboration meant that all the organisations involved learned alot and challenged themselves on other forms of discrimination and exclusion that had been outside their immediate "sphere." It also meant there were other eyes, ears and mouths out there to tip me off about issues relevant to feminism or present a feminist perspective in situations where feminist organisations weren't represented.
I think in these uncertain economic times, the tendency may be to put the wagons in a circle and turn inwards, focussing on what impacts on "me and mine" first and foremost. I understand where that's coming from, but I think it can be self-defeating if we all become fragmented, our voices weaker and expending our energies as much on dukeing it out with groups who experience oppression (and even with other feminists, for pity's sake!)